It is not in the scope of this elementary textbook to introduce quantum mechanics in detail or to provide an elaborate mathematical background required for quantum computing. However, we will provide some basic ideas that are essential for us to proceed further. To be precise, here we will briefly describe vector space, different types of operators, Gram-Schmidt procedure, postulates of quantum mechanics, POVM, density operator, entanglement and its measures, partial trace, Schmidt decomposition, Bloch sphere, nocloning theorem, etc. Let us start our journey toward the world of quantum computation by reviewing some simple ideas of algebra.