# Reference: Representation Theory

In studying Linear Representation theory of finite groups, many authors state the important theorems over the field $\mathbb{C}$ or algebraically closed field, which is much stronger assumption. I am interested in representations over general fields. I know that we have, atleast to consider cases where characteristic of field is zero or prime to $|G|$ (ordinary representations) and characteristic dividing $|G|$ (modular representations).

I would like to see the important concepts such as "Schur's Lemma, Maschke's theorem, McKay irreducibility criteria, orthogonality relations, number of irreducible $F$-representations and number of some type of conjugacy classes of group etc (in ordinary case at least).

Can someone suggest some good reference for the subject which states these results with weaker hypothesis (means not always consider algebraically closed field)?

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