Abstract: The study of Quantum Computing necessitates careful examination of the most fundamental questions of Quantum Theory, such as the measurement problem, and may lead to important advances in practical applications such as cryptography, search, and optimization. In order for a Quantum Computer to be practically useful, the design must be scalable to hundreds of quantum bits, or qubits, while maintaining quantum coherence. Qubits constructed from superconducting electronics are promising because of their inherent scalability using established nano-fabrication techniques. Superconducting qubits based on the flux degree of freedom are insensitive to noise from charge fluctuations and can be read-out using a Superconducting Quantum Interference Device (SQUID). When properly designed, a superconducting loop interrupted by three Josephson junctions acts as a quantum two-state system. In this Dissertation, an exact calculation of the energy levels of the three junction flux qubit is used to design samples consisting of one or two qubits to investigate coherence properties. Careful attention is given to the system electronics to minimize external sources of noise acting back on the qubit that result in decoherence. We report measurements on two superconducting flux qubits coupled to a readout SQUID. Two on-chip flux bias lines allow independent flux control of any two of the three elements, as illustrated by a two-dimensional qubit flux map. The application of microwaves yields a frequency-flux dispersion curve for 1- and 2-photon driving of the single-qubit excited state and reveals spurious resonances intrinsic to each qubit. Coherent manipulation of the single-qubit state results in Rabi oscillations, Ramsey fringes, and Hahn spin-echos. This information is used to develop a model of the decoherence caused by the interaction of the qubit with its environment. A detailed model for the interaction of a flux qubit with a readout SQUID predicts the resolution of a measurement and its effect on the qubit. Two adjustable inter-qubit coupling systems that can produce bipolar coupling strength are presented. These systems can be used to produce the quantum Controlled-NOT gate, which when combined with single qubit operations forms a basis for Universal Quantum Computation.