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HTML 

              
                <div class='ui'>
  <div class='multiperiodos-component'>
    <ul>
      <li data-id='1' data-start='01/01/2018' data-end='30/06/2018'>
        <div class='period'>
          <a href='#' class='edit-period' onclick='edit(this)'><i class="material-icons">mode_edit</i> 01/01/2018 a 30/06/2018</a>
          <a href='#' class='handle' tooltip='Arraste e solte para reordenar' flow='up'><i class="material-icons">drag_handle</i></a>
          <a href='#' class='delete tip_red' tooltip='Remover período' flow='up' onclick='remove(this)'><i class="material-icons">remove_circle</i></a>
        </div>
        <div class='edit hided'>
          <a href='#' class='cancel' tooltip='Cancelar edição' flow='up' onclick='cancel(this)'><i class="material-icons">clear</i></a>
          <input type='text' value='' placeholder='data inicial' class='date-start'><span>até</span> 
          <input type='text' value='' placeholder='data final' class='date-end'>
          <a href='#' class='add' tooltip='Atualizar período' flow='up' onclick='save(this)'><i class="material-icons">check_circle</i></a>
        </div>   
      </li>
      <li>
        <a href='#' class='bt-new' onclick='addNew(this,999)'>Adicionar um período <i class="material-icons">add_circle</i></a><a href='#' class='bt-new-options' onclick='openPoplist(this)'><i class="material-icons">arrow_drop_down</i></a>
      </li>
    </ul>
  </div>
</div>

  <div class='poplist hided'>
    <ul>
      <li onclick='addNew(this,0)'>Este mês</li>
      <li onclick='addNew(this,1)'>Último mês</li>
      <li onclick='addNew(this,3)'>Último trimestre</li>
      <li onclick='addNew(this,6)'>Último semestre</li>
      <li onclick='addNew(this,6)'>Último ano</li>
      <li onclick='addNew(this,999)'>Outro período</li>
    </ul>
  </div>
!

CSS 

              
                /*--------------------
General Styles
---------------------*/

*,
*::before,
*::after {
  -webkit-box-sizing: border-box;
  box-sizing: border-box;
  margin: 0;
  padding: 0;
  border: 0;
  font-size: 100%;
  font: inherit;
  vertical-align: baseline;
  text-rendering: optimizeLegibility;
  -webkit-font-smoothing: antialiased;
  -webkit-user-select: none;
  user-select: none;
}

body {
  font-family: 'Open Sans', sans-serif;
  font-size: 12px;
  background: #f4f5f9;
}

a {
  text-decoration: none;
  display: inline-block;
}

input[type=text]{
  outline: 0;
  height: 31px;
  width: 80px;
  color: #3B3B3B;
  text-align: center;
  border: 1px solid #D6D6D6;
  border-radius: 3px;
  display: inline-block;
  background: #FFF;
  padding: 8px 8px;
  -webkit-user-select: all;
  -moz-user-select: all;
  -ms-user-select: all;
  user-select: all;
}

input[type=text]:focus {
    outline: none;
}

input::-webkit-input-placeholder {
    color: #999;
}

input:focus::-webkit-input-placeholder {
    color: transparent;
}

.ui {
  width: 305px;
  padding: 20px;
  position: absolute;
  top: 45%;
  left: 50%;
  background-color: #fff;
  
  transform: translate(-50%, -50%);
  border-radius: 6px;
  box-shadow: 0 30px 48px rgba(50,54,70,0.24);
}

.hided {
  display: none;
}

/*--------------------
Component
---------------------*/

.multiperiodos-component{
  width: 265px;
  background: #FFFFFF;
  border: 1px solid #E0E0E0;
  border-radius: 3px;
}

.multiperiodos-component ul{
  list-style: none;
  margin: 0;
  padding: 0;
}

.multiperiodos-component li{
  
}

.multiperiodos-component li:nth-child(odd){
  position: relative;
}

.multiperiodos-component li:nth-child(odd){
  background-color: #fafafa;
}

.multiperiodos-component li:last-child{
  border-top: 1px solid #ffffff;
  background-color: #f5f5f5;
  text-align: center;
}

.period, .bt-new{
  height: 35px;
  line-height: 25px;
  padding: 5px 10px;
  z-index: 0;
  transition: all 0.6s;
}

.period a{
  color: #1E88E5; /*Blue 600*/
}

.period a > i{
  font-size: 18px;
  float: left;
  margin-right: 5px;
  margin-top: 3px;
}

a.handle, a.delete{
  float: right;
}

a.handle{
  color: #9E9E9E;
  margin-top: -2px;
}

a.handle > i {
  font-size: 24px;
}

a.delete{
  color: #EF5350; /*Red 400*/
  margin-right: 5px;
  margin-top: -1px;
  visibility: hidden;
}

a.delete:hover{
  color: #D32F2F; /*Red 700*/
  cursor: pointer;
}

a.delete > i {
  font-size: 22px;
}

.period:hover > a.delete{
  visibility: visible;
}

li:first-child > .period:hover > a.delete{
  
}

.edit{
  position: absolute;
  top: 0px;
  height: 35px;
  width: 100%;
  padding: 2px 10px;
  z-index: 1;
}

a.cancel{
  color: #9E9E9E; /*Gray 500*/
  line-height: 30px;
  float: left;
  margin-right: 3px;
  margin-top: 6px;
}

a.cancel:hover{
  color: #424242; /*Gray 800*/
  cursor: pointer;
}

a.cancel > i{
  font-size: 18px;
  float: left;
  margin-right: 2px;
}

a.add{
  color: #4B2F7E; /*Purple 900*/
  float: right;
  margin-right: 5px;
  margin-top: 4px;
}

a.add:hover{
  color: #3E2F68; /*Purple 1000*/
  cursor: pointer;
}

a.add > i{
  font-size: 22px;
}

.edit > span{
  display: inline-block;
  margin: 0 3px;
}

input[type=text]{
  outline: 0;
  height: 31px;
  width: 80px;
  color: #3B3B3B;
  text-align: center;
  border: 1px solid #D6D6D6;
  border-radius: 3px;
  display: inline-block;
  background: #FFF;
  padding: 8px 8px;
  -webkit-user-select: all;
  -moz-user-select: all;
  -ms-user-select: all;
  user-select: all;
}

input[type=text]:focus {
    outline: none;
}

input::-webkit-input-placeholder {
    color: #999;
}
input:focus::-webkit-input-placeholder {
    color: transparent;
}

a.bt-new, a.bt-new-options{
  color: #4B2F7E; /*Purple 900*/
  font-weight: 700;
}

a.bt-new:hover, a.bt-new-options:hover{
  color: #3E2F68; /*Purple 1000*/
  cursor: pointer;
}

a.bt-new > i {
  font-size: 22px;
  float: left;
  margin-right: 5px;
}

a.bt-new-options {
  display: inline-block;
  float: right;
  margin-right: 5px;
  width: 45px;
  height: 35px;
  text-align: center;
  border-left: .5px solid #fff;
}

a.bt-new-options > i {
  font-size: 22px;
  margin-top: 7px;
}


/*--------------------
Poplist
---------------------*/

.poplist {
  width: 265px;
  padding: 5px 0;
  position: absolute;
  top: 20px;
  left: 20px;
  background-color: #fff;
  border-radius: 6px;
  border: 1px solid #eee;
  box-shadow: 0 15px 24px rgba(50,54,70,0.16);
  overflow: hidden;
}

.poplist ul{
  list-style: none;
  margin: 0;
  padding: 0;
}

.poplist li{
  background-color: #fff;
  color: #212121;
  line-height: 26px;
  padding: 0 10px;
}

.poplist li:hover{
  background-color: #3E2F68; /*Purple 1000*/
  color: #fff;
  line-height: 26px;
  padding: 0 10px;
  cursor: pointer;
}



/*--------------------
Tooltip
---------------------*/

[tooltip] {
  position: relative;
}

/* Applies to all tooltips */
[tooltip]::before,
[tooltip]::after {
  text-transform: none;
  font-size: 12px;
  font-weight: 600;
  line-height: 1.2;
  user-select: none;
  pointer-events: none;
  position: absolute;
  display: none;
  opacity: 0;
}
[tooltip]::before {
  content: '';
  border: 5px solid transparent;
  z-index: 22; /* absurdity 1 */
}
[tooltip]::after {
  content: attr(tooltip); /* magic! */
  text-align: center;

  /*
    Let the content set the size of the tooltips
    but this will also keep them from being obnoxious
  */
  min-width: 88px;
  max-width: 218px;
  /* white-space: initial;
  overflow: hidden;
  text-overflow: ellipsis; */
  padding: 6px;
  border-radius: 2px;
  box-shadow: 0 1em 2em -.5em rgba(0, 0, 0, 0.35);
  background: #3E2F68;
  color: #fff;
  z-index: 21; /* absurdity 2 */
}

/* Make the tooltips respond to hover */
[tooltip]:hover::before,
[tooltip]:hover::after {
  display: block;
}

/* don't show empty tooltips */
[tooltip='']::before,
[tooltip='']::after {
  display: none !important;
}

/* FLOW: UP */
[tooltip]:not([flow])::before,
[tooltip][flow^="up"]::before {
  bottom: calc(100% + 3px);
  border-bottom-width: 0;
  border-top-color: #3E2F68;
}
[tooltip]:not([flow])::after,
[tooltip][flow^="up"]::after {
  bottom: calc(100% + 8px);
}
[tooltip]:not([flow])::before,
[tooltip]:not([flow])::after,
[tooltip][flow^="up"]::before,
[tooltip][flow^="up"]::after {
  left: 50%;
  transform: translate(-50%, -.5em);
}

a[class~="tip_red"][tooltip]::after {
  background: #F75E5E;
}
a[class~="tip_red"][tooltip][flow^="up"]::before {
  border-top-color: #F75E5E;
}

/* KEYFRAMES */
@keyframes tooltips-vert {
  to {
    opacity: .9;
    transform: translate(-50%, 0);
  }
}

@keyframes tooltips-horz {
  to {
    opacity: .9;
    transform: translate(0, -50%);
  }
}

/* FX All The Things */
[tooltip]:not([flow]):hover::before,
[tooltip]:not([flow]):hover::after,
[tooltip][flow^="up"]:hover::before,
[tooltip][flow^="up"]:hover::after {
  animation: tooltips-vert 300ms ease-out forwards;
}
!

JS 

              
                

$('.date-start').mask("00/00/0000", {placeholder: "data inicial"});
$('.date-end').mask("00/00/0000", {placeholder: "data final"});

var edit = function(el){
  var $period = $(el).parent();
  var $edit = $period.parent().find(".edit");
  var $edit_period = $period.find(".edit-period");
  
  var text_period = $edit_period.html();
  text_period = text_period.replace('<i class="material-icons">mode_edit</i> ','');
  console.log(text_period);
  var date_start = text_period.substring(0,10);
  var date_end = text_period.substring(text_period.length - 10,text_period.length);
  console.log('date_start '+date_start+' :: date_end '+date_end);
  $edit.find(".date-start").val(date_start);
  $edit.find(".date-end").val(date_end);
  
  $period.addClass("hided");
  $edit.css("position", "relative");
  $edit.removeClass("hided"); 
};

var cancel = function(el){
  var $edit = $(el).parent();
  $edit.addClass("hided");
  $edit.parent().find(".period").removeClass("hided"); 
};

var save = function(el){
  var $edit = $(el).parent();
  var $period = $edit.parent().find(".period");
  var text_period = $edit.find(".date-start").val() + ' a ' + $edit.find(".date-end").val();
  
  $edit.addClass("hided");
  $period.find(".edit-period").html('<i class="material-icons">mode_edit</i> '+text_period);
  $period.removeClass("hided"); 
};

var remove = function(el){
  var $period = $(el).parent();
  var $li = $period.parent();
  $li.remove();
  positionPoplist();
};

var addNew = function(el,month){
  var $li = $(el).parent();
  
  if(!$(el).hasClass('bt-new')){
    $li = $('.bt-new').parent();
  }
  
  var $edit = $li.find(".edit");
  
  var date_format = 'dd/MM/yyyy';
  var isCustomPeriod = false;
  
  if(month == 999){ 
    month = 0; 
    isCustomPeriod = true;
  }
  
  var first_day = new Date();
  first_day.setDate(1);
  first_day.setMonth(first_day.getMonth()-month);
  
  var last_day = new Date();
  if( month > 0 ){
    last_day.setMonth(last_day.getMonth(), 0);
  }
  var date_start = $.format.date(first_day, date_format);
  var date_end = $.format.date(last_day, date_format);
  
  console.log('date_start '+date_start+' :: date_end '+date_end);
  
  var new_id = $('.multiperiodos-component ul').length +1;
  
  var code = "<li data-id='"+ new_id +"' data-start='"+ date_start +"' data-end='"+ date_end +"'><div class='period'><a href='#' class='edit-period' onclick='edit(this)'><i class='material-icons'>mode_edit</i> "+ date_start +" a "+ date_end +"</a><a href='#' class='handle' tooltip='Arraste e solte para reordenar' flow='up'><i class='material-icons'>drag_handle</i></a><a href='#' class='delete tip_red' tooltip='Remover período' flow='up' onclick='remove(this)'><i class='material-icons'>remove_circle</i></a></div><div class='edit hided'><a href='#' class='cancel' tooltip='Cancelar edição' flow='up' onclick='cancel(this)'><i class='material-icons'>clear</i></a><input type='text' value='"+ date_start +"' placeholder='data inicial' class='date-start'><span>até</span><input type='text' value='"+ date_end +"' placeholder='data final' class='date-end'><a href='#' class='add' tooltip='Atualizar período' flow='up' onclick='save(this)'><i class='material-icons'>check_circle</i></a></div></li>";
  $(code).insertBefore($li);
  
  if( isCustomPeriod ){ 
    edit( $li.prev().find('.edit-period') ); 
  };
  
  positionPoplist();
  closePoplist();
};

var openPoplist = function(el){
  var $poplist = $('.poplist');
  
  if($poplist.hasClass('hided')){
    positionPoplist();
    $poplist.removeClass("hided");
  } else {
    closePoplist();
  }
};

var positionPoplist = function(){
  var $ui = $('.ui');
  var $poplist = $('.poplist');
  var position = $ui.position();
  var positionTop = ($ui.height() + position.top);
  $poplist.css("top",positionTop+21);
  $poplist.css("left",position.left+20); 
};

var closePoplist = function(){
  $('.poplist').addClass("hided"); 
};

$(window).on('resize', function(){
  positionPoplist();
});
!
999px

Console