This book presents basic results in Group theory and Lattice theory. The initial chapters cover topics such as Lattice and types of Lattice. The later chapters contain some additional topics such as Ring, Field, Ideal. The Topics have been presented in a simple form, with a number of examples. Proof have been made direct and simple, omitting irrelevant details. The book has evolved out of teaching over a period of years and can serve as text book on Distributive and modular Lattice.