  Operads are algebraic devices offering a formalization of the concept of
operations with several inputs and one output. Such operations can be naturally
composed to form bigger and more complex ones. Coming historically from
algebraic topology, operads intervene now as important objects in computer
science and in combinatorics. The theory of operads, together with the
algebraic setting and the tools accompanying it, promises advances in these two
areas. On the one hand, operads provide a useful abstraction of formal
expressions, and also, provide connections with the theory of rewrite systems.
On the other hand, a lot of operads involving combinatorial objects highlight
some of their properties and allow to discover new ones.
  This book presents the theory of nonsymmetric operads under a combinatorial
point of view. It portrays the main elements of this theory and the links it
maintains with several areas of computer science and combinatorics. A lot of
examples of operads appearing in combinatorics are studied and some
constructions relating operads with known algebraic structures are presented.
The modern treatment of operads consisting in considering the space of formal
power series associated with an operad is developed. Enrichments of
nonsymmetric operads as colored, cyclic, and symmetric operads are reviewed.
  This text is addressed to any computer scientist or combinatorist who looks a
complete and a modern description of the theory of nonsymmetric operads.
Evenly, this book is intended to an audience of algebraists who are looking for
an original point of view fitting in the context of combinatorics.
