In this note I present some of the main ideas of finite group theory, starting with examples of non-abelian groups (groups of matrices and groups of permutations), going to Galois theory, i.e. the way polynomials and groups interact, and finally simple groups, solvable groups and their role in under- standing when the roots of a polynomial can be expressed by starting with the coefficients and performing sums, differences, products, divisions and root extractions.
Ideas in finite group theory File in PDF.