This dissertation is devoted to three main subjects: 
In the first part, an algorithm to calculate the multi-pulse EPR signals including COSY (Correlation Spectroscopy), two-pulse DQ (Double Quantum), five-pulse DQM (Double Quantum Modulation), four-, five-, six-pulse DQC (Double Quantum Coherence) is developed. The applicability of each of these pulse sequences is further studied. 
In addition, a novel method based on doubly rotating frames (DRF) has been exploited to calculate three- and four-pulse DEER (Double Electron-Electron Resonance) signals for a system of two dipolar-coupled nitroxides on a sample of bis-nitroxide nanowire, P1, in deuterated ortho-terphenyl solvent with 5% BnPy (d14-oTP/BnPy) as well as two coupled Gd^{3+} ions in Gd ruler 1_5 in D_2O/glycerol-d_8 (7/3 volume ratio). The technique is then used to calculate the basis kernel signals accurately by numerical techniques to obtain the probabilities of distance distribution, P\left(r\right),\ using Tikhonov regularization and DeerAnalysis software. 
In the second part, two models, namely cylindrical and conical models of fluctuation, are presented wherein one considers the random fluctuations in the \widetilde{g} and \widetilde{A}  matrices of the spin Hamiltonian due to thermal motion of malonic acid molecule. Accordingly, the relaxation matrix is calculated in Liouville space for the four-level coupled electron-nuclear spin system, using the formalism outlined by (Lee, Patyal and Freed 1993). The obtained relaxation matrix is then used to calculate the time-dependent echo-ELDOR signal by solving the relevant Liouville-von Neumann (LVN) equation. 
In the third part, the relaxation during free evolution and many-body effects in a SECSY signal, including instantaneous and spectral diffusions, which are due to the dipolar interaction between an electron with other electrons in a \gamma-irradiated malonic acid crystal are investigated.