I'm a junior and i have never leanred this subject.
I think "Lie Group&Algebra" is really deep and massive theory since the wikipedia page for it is quite long.
Nevertheless, i'm not sure whether this subject is taught in department of mathematics. If so, in which grade one can learn this subject? (I have skimmed a book in a library and i see that the general theory in the context of manifold, requires quite a lot preliminaries)
I heard that physicists deal with this group all time since everything they are dealing with can be modeled as a lie group. However, to which part of mathematics does the subject "Lie group" belong to? PDE?
I'm interested in pure and soft mathematics not like PDE. So would it be completely fine not to prepare to study this subject?
It is a topic that belongs to the broad subject of abstract algebra. It also has deep connections with plenty of other areas of mathematics and has shown itself to be a very powerful language for doing Quantum physics.
Usually courses that teach you the topics of Lie Groups and Lie algebras are title "Lie groups" or some variation. You might get a taste of them in a standard undergraduate abstract algebra course but this seems to be unlikely.
It is a topic that should be approached after gaining some firm foundation with other algebraic structures and notions such as groups, rings, fields, modules, algebras, etc.
But this is not to discourage, it is a very rich subject and worth taking the time to learn.