Block ciphersarecryptographicprimitivesthatoperateon fixed sizetexts(blocks). Mostdesigns aim towards secure andfastencryption oflarge amounts ofdata. Block ciphers also serve as the building block of a number of hash functions and message authentication codes(MAC).Thetask of cryptanalysisisto ensurethat no attack violatesthe securitybounds specifiedbygeneric attack namely exhaustivekey search and table lookup attacks. This thesis contains a general introduction to cryptography with focus on block ciphers and important block cipher designs, in particular the Advanced Encryption Standard(AES).Wedescribe the mostgeneraltypes ofblock cipher cryptanalysis but concentrate on the algebraic attacks. While the algebraic techniques have been successful oncertainstreamcipherstheirapplicationtoblock ciphershasnot shown any significant results so far. This thesis contributes to the field of algebraic attacks on block ciphers by an analytic and systematic approach that allows insight to the techniques. Moreover a new procedure of generating and applying probabilistic equations in algebraic attacks on block cipher is proposed and examined. Also, we present practical results, which to our knowledge are the best algebraic results on small scale variants of AES. In the final part of the thesis we present a new block cipher proposal Present and examine its security against algebraic and differential cryptanalysis in particular.