Properties
of real and complex numbers, Binary Operation, Bijective maps, Inversion
Theorem, Isomorphic binary structures, Groups, Examples of Groups, Uniqueness
of identity and inverse, Elementary properties of groups, Abelian Groups, Order
of a Group, Finite Groups, Subgroups, Examples of subgroups, Two Step subgroup
test, One Step subgroup test, Cyclic Groups,

Permutation
Groups, Examples of Permutation Groups, Theorem on permutation groups, Cayley''s
Theorem, Orbits, Cycles, Disjoint Cycles, Cycle Decomposition, Parity of
permutations, Alternating Group, Direct product, Finitely generated abelian
groups, Cosets, Partition of group

Lagrange''s
Theorem, Applications of Lagrange''s theorem, Indices of subgroups, Converse of
Lagrange''s Theorem, Homomorphism of Groups, Properties of homomorphism, Normal
Subgroups, Morphism Theorem for groups, Application of Morphism theorem, properties
of homomorphism, Normality of kernel of homomorphism, Normal group, Factor
group, Cosets multiplcation & Normality

Examples on
kernel of homomorphisms and group homomorphism, Factor group from homomorphism,
Kernel of an injective homomorphism, Factor groups from Normal subgroups, Example
of Morphism theorem of groups, Normal groups and Inner Automorphism, Factor
group computations

Simple
Group, Maximal Normal Subgroups, The Centre subgroup, Example of the Centre
subgroup, Commutator subgroup, Generating set, Commutator subgroup, Automorphisms,
Group Action on set, Stablizer, Orbits, Conjugacy and G-sets

Isomorphism
Theorem, Second Isomorphism Theorem, Third Isomorphism Theorem, First Sylow
Theorems, Second Sylow Theorems, Third Sylow Theorems, Application of Sylow
Theorems