Can I use twitter bootstrap without jquery?

Twitter bootstrap itself isn't jQuery dependant.

If you use just the CSS part of it, you won't need jQuery.

If you use the Javascript plugins you need jQuery, since they are jQuery plugins.

v3: http://getbootstrap.com/javascript/

v4: https://getbootstrap.com/docs/4.0/getting-started/javascript/

Short answer is yes but as Bruno says, the jQuery plugins won't work. To workaround this, I made a small replacement script so the dropdown menus, alert boxes and collapsible nav bar will work without jQuery: http://daniemon.com/blog/bootstrap-without-jquery/

Yes you can via Native Javascript for Bootstrap. Enjoy