The aim of this book is to explore the algebraic and combinatorial properties of simplicial complexes. Let S = k[x1, x2, ..., xn] be a polynomial ring over an infinite field k. Note that, there is a natural bijection between the square-free monomial ideals (so called non facet ideals) and simplicial complexes introduced by R.P. Stanley. Later Faridi introduced another correspondence betweeen the square-free monomial ideals (so called facet ideals) and simplicial complexes. So, corresponding to a square-free monomial ideal I in S, one can consider I as the facet ideal of one simplicial complex and as the non-face ideal for another . In this book, we mainly discuss the invariants between these two simplicail complexes. Also we have discuss about a new class of ideals called f-ideals and its properties.