In this dissertation, the nature of magnetism in transition-metal-doped phthalocyanines (TMPc, TM = Co, Ni, Cu, V, and Mn, chemical formula: C 32H16N8TM) is investigated by measuring their magnetization (M) and ac susceptibilities in magnetic fields up to 90 kOe and covering the wide temperature range of 0.5 K to 300 K. These low temperatures and high magnetic field measurements combined with detailed analysis of the data have provided new information about the nature of magnetism of TMPc. The powder samples used here were structurally characterized using x-ray diffraction and scanning electron microscopy.;TMPc are a class of organic semiconductors with potential applications in spintronics and they are planar molecules with the TM atom at the center bound to four N atoms and forming a linear chain along the monoclinic b-axis. Because of this symmetry, the ground states of TMPc often violate the Hunds' rules; e.g. the S = 3/2 state for d5 Mn(II) in beta-MnPc, S = 1/2 state for the d7 Co(II) in beta-CoPc, and S = 0 state for the d8 Ni(II) in NiPc. The magnetic properties of TMPc are also affected by the stack angle delta between the orientation of the molecular plane and the b-axis, delta being 65° (45°) for alpha (beta) phase.;For both alpha-CuPc and beta-CuPc, M vs. T data fit well with the Bonner-Fisher model for S = 1/2 antiferromagnetic (AFM) Heisenberg linear chain yielding the Cu2+-Cu2+ exchange constant Jex/kB = - 1.7 K (- 0.2 K) for alpha-CuPc(beta-CuPc). This order of magnitude difference in Jex/kB is likely due to the smaller Cu2+-Cu2+ distance in alpha-phase than in beta-phase. The M vs. H at 2 K and 5 K data are interpreted including the effect of the exchange coupling.;For beta-CoPc, the predicted peak in chi vs. T data by Bonner-Fisher model was observed at Tmax = 1.9 K for the first time yielding the Heisenberg exchange constant Jex/kB = - 1.5 K between the Co2+-Co2+ ions. The isothermal data of M vs. H at 1 K shows good agreement with the Bonner-Fisher model; M vs. H at 5 K data is interpreted by including the effect of the exchange interaction.;For VOPc (phase II), the analysis of the M vs. T data shows VO 2+ electronic state with spin S = 1/2 and theta = - 0.1 indicates a very weak AFM exchange coupling between neighboring VO2+ ions which implies the near-perfect paramagnetism of VOPc. This conclusion is also supported by the analysis of the M vs. H data at several temperatures. The diamagnetic nature of beta-NiPc corresponding to the S = 0 state for the 3d8 Ni(II) is confirmed by measurements and analysis of the magnetization with temperature-independent susceptibility chiD = - 3.38 x 10-7 emu/gOe. The observed ferromagnetic component in the beta-NiPc powder sample is identified with Fe impurity.;For beta-MnPc with S = 3/2, detailed analysis of the dc and ac susceptibilities leads to the conclusion of the absence of 3-dimensional long range magnetic ordering in this system contrary to previous reports. This conclusion is supported by the Arrott plots and lack of a peak in the ac susceptibilities and specific heat near the quoted TC ≈ 8.6 K. Instead, beta-MnPc is best described as an Ising-like chain magnet with Arrhenius relaxation of the magnetization governed by an intra-layer ferromagnetic exchange constant Jex/kB = 2.6 K and the single ion anisotropy energy constant |D|/kB = 8.3 K. The absence of 3D long-range ordering is consistent with the measured |D| being >Jex.