Note for group representation theory

I made this note when reading the book Introduction to the representations of groups and algebras by Feng Keqin, Zhang Pu and Li Shangzhi. This note covers:
   1. Basic definitions in group representation theory, construction of representations, completely reducible and irreducible representations, Schur lemma and Maschke theoren
  2. Character theory, orthogonal property, more on irreducible representations(dimension, amounts), deciding character table, application: Burnside theorem
  3. Basic definitions on modules and algebras, Wedderburn-Artin theorem on semi-simple module/algebra, Jacobson radical
  4. Projective and injective module, absolutely simple module and splitting field, ultimate goal: irreducible character decides irreducible representations
  5. Induced representations, Frobenius reciprocity law, Mackey subgroup theorem and irreducibility of induced representations   
  6. Representations of compact group, Peter-Weyl theorem: applications and proof.
One can also refer the lecture notes by Prof. Yang Jinbang.