Complexity theory is a branch of theoretical computer science that studies the intrinsic difficulty of computational problems. It focuses on classifying problems based on their computational complexity, which is the amount of resources required to solve them, such as time and space. Complexity theory also explores the relationships between different classes of problems, the existence of complete and hard problems, and the limits of efficient computation. The theory is foundational for understanding the capabilities and limitations of algorithms and has applications in fields such as cryptography, optimization, and artificial intelligence.