I wanted to know what is the name of this kind of jacket, the blue one with golden buttons.
I would call it a military-style jacket (see Google Image search in link for many examples).
Key features are the close fit, brass buttons, epaulets (shoulder things), the stand-up collar, and the single-breasted front with buttons all the way up to the neck.
Of course military uniforms vary tremendously (think of bomber jackets or modern camouflage), but variations on this style have been popular in a surprisingly wide array of militaries for the past century or so. You can see many examples in the Imperial War Museum's collections, such as this 1907 imperial Russian artillery jacket:
And this contemporary US Navy dress uniform: