This book presents a collection of 36 pieces of scientific work in the field of complexity theory and basic cryptography: 20 contributions of research, survey articles 13, and 3 points of view report program and reflective. Particular topics dealt with include the average case complexity, the complexity of the approach, derandomization, expander graphs, hashing function, the local code was tested, machines that take advice, NP-completeness, one-way function, probabilistically checkable proof, proof of knowledge, property testing, pseudorandomness , randomness extractors, sampling, trapdoor permutations, zero-knowledge, and non-iterative zero knowledge. All in all, this potpourri of study in complexity and cryptography is the most valuable contribution to the field of theoretical computer science centered around personal achievement and the views from one of the outstanding representatives.