New methods for optimum separation of (2)H MAS NMR spectra are presented. The approach is based on hypercomplex spectroscopy that is useful for sign discrimination and phase separation. A new theoretical formalism is developed for the description of hypercomplex experiments. This exploits the properties of Lie algebras and hypercomplex numbers to obtain a solution to the Liouville-von Neumann equation. The solution is expressed in terms of coherence transfer functions that describe the allowed coherence transfer pathways in the system. The theoretical formalism is essential in order to understand all the features of hypercomplex experiments. The method is applied to the development of two-dimensional quadrupole-resolved (2)H MAS NMR spectroscopy. The important features of this technique are discussed and two different versions are presented with widely different characteristics. An improved version of two-dimensional double-quantum (2)H MAS NMR spectroscopy is developed. The conditions under which the double-quantum experiment is useful are discussed and its performance is compared with that observed for the quadrupole-resolved experiments. A general method is presented for evaluating the optimum pulse sequence parameters consistent with maximum sensitivity and resolution. This approach improves the performance of the experiments and is essential for any further development of the techniques. The effects of finite pulse width and hypercomplex data processing may lead to both intensity and phase distortions in the spectra. These effects are analyzed and general correction procedures are suggested. The techniques are applied to polycrystalline malonic-acid-(2)H(4) for which the spinning sideband manifolds from the carboxyl and methylene deuterons are separated. The spinning sideband manifolds are simulated to determine the quadrupole parameters. The values are consistent with previous results, indicating that the techniques are both accurate and reliable.