<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
<script>
$("#button").click(function(e) {
  e.preventDefault();
  $.ajax({
    type: "POST",
    url: "kaydet.php",
    data: $("#form1").serialize()
  }).done(function(data) {
    alert("Form gönderildi. Kaynak: " + data);
  });
});
</script>