In this thesis, I present basic concepts of quantum mechanics needed to understand quantum circuits and algorithms, which I then describe at a fundamental level. I start with the linear algebra necessary for the description of quantum mechanics, and then I introduce the fundamental unit of quantum computation, the qubit. Afterwards I talk about quantum operators, and how they are used in quantum algorithms such as dense coding and so on. Finally, I devote the last section called ’Quantum state preparation’ to a way of constructing a quantum circuit for building any state of arbitrary number of qubits, which I explored together with my supervisor András Kruppa.