Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.
Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.
Covers the properties of the exponential map in Lie groups and their algebras, including smoothness and the relationship between subgroups and algebras.