  This tutorial aims at giving an introductory treatment of the circuit
analysis of superconducting qubits, i.e., two-level systems in superconducting
circuits. It also touches upon couplings between such qubits and how microwave
driving and these couplings can be used for single- and two-qubit gates, as
well as how to include noise when calculating the dynamics of the system. We
also discuss higher-dimensional superconducting qudits. The tutorial is
intended for new researchers with limited or no experience with the field but
should be accessible to anyone with a bachelor's degree in physics. The
tutorial introduces the basic methods used in quantum circuit analysis,
starting from a circuit diagram and ending with a quantized Hamiltonian, that
may be truncated to the lowest levels. We provide examples of all the basic
techniques throughout the discussion, while in the last part of the tutorial we
discuss several of the most commonly used circuits for quantum-information
applications. This includes both worked examples of single qubits and examples
of how to analyze the coupling methods that allow multiqubit operations. In
several detailed appendices, we provide the interested reader with an
introduction to more advanced techniques for handling larger circuit designs.
