Deal all, I am looking for a gentle introduction to algebraic invariant theory (for a Bachelor project) with some simple (but interesting) applications in representation theory (of finite groups, of Lie algebras). Thanks for your help!
A good book is the book Lie Groups, An Approach through Invariants and Representations" by Claudio Procesi. This contains algebraic invariant theory, Lie algebras, representations of finite groups and of Lie algebras, and much more. It should be ideal for your purpose.