Hidden symmetry in classical and quantum physics

In the present work I study spontaneous symmetry breaking. This interesting phenomenon is an important part of the elementary particle physics and thanks to it, it is possible to generate masses of fermions and gauge bosons in the Standard Model. However, in this work I try to present a more general view and I bring up a few examples from various parts of physics, starting with classical mechanics and ending with quantum eld theory. I also study consequences of spontaneous symmetry breaking and discuss dierences in manifestations of this phenomenon in theories with nite and innite number of freedom. This work is primarily meant as a consistent survey of already known results supplemented with their sueciently detailed technical derivation in a comprehensible form