Bringing together research that was otherwise scattered throughout the literature, this book collects the main results on the conditions for the existence of large algebraic substructures. Many examples illustrate lineability, dense-lineability, spaceability, algebrability, and strong algebrability in different areas of mathematics, including real and complex analysis. The book presents general techniques for discovering lineability in its diverse degrees, incorporates assertions with their corresponding proofs, and provides exercises in every chapter.