It is quite well known that Complex number is the sum of a real and imaginary number. We however, present another quantity called Mixed Number (MN), which is the sum of a scalar and a vector that may be considered as an extension of complex number. The algebra of Mixed number ? the operations of addition, multiplication etc. are defined while addition and multiplication of Mixed numbers are associative. An attempt has been made to study MN algebra to compare both quaternion algebra and geometric product as well as to observe some of it application. It has been observed that MN algebra is consistent with Pauli matrix algebra, a convenient tool to handle Dirac electron theory. In this book some applications of Mixed number has been studied in detail. We have applied Mixed number in the following cases: (1) In Quantum Mechanics: Here we have figured out the Displacement operator, Vector differential operator, Angular momentum operator and Klein-Gordon equation in terms of MN algebra. (2) In Electrodynamics: In this case Maxwell?s equations have been written using Mixed number algebra. (3) A ?Mixed number Lorentz Transformation? has been developed. This transformation is associative.