A goal of writing a book is to introduce an alternative and rich mathematical framework, grounded on building simplicial complexes, for tackling the problems emerging from complex systems research. Another goal is to introduce alternative mathematical tools, based on the relationships between simplices, for discovering new, previously hidden, features of complex systems. The motivation that led us to write this book is actually twofold. First, there is a lack of literature that covers the extensive applications of simplicial complexes, which are not restricted to topological data analysis or qualitative structural analysis. Second, we aim to introduce the reader to algebraic topology concepts straightforwardly and intuitively, which is sufficient for simple applications and provides a solid foundation for further expanding knowledge.