This experimental research project is devoted to unusual magnetic behavior in pure and doped spin-gap systems, and in spin-liquid systems, as studied by muon spin relaxation. Of principal interest are low-dimensional and/or geometrically frustrated spin systems. Of interest are conditions for the formation/absence of spin freezing, the role of frustration, and effects of charge doping and magnetic dilution. In more detail, four topics and systems of interest are: 1) questions of ordering temperature and/or ordered moment size in quasi 1-d zig-zag spin chain SrCuO2 and LixV2O5; 2) charge/vacancy doping effects in 2-leg ladders Sr2(Cu,Zn)4O6, LaCuO2.5, and (Ca,Mg)(V,Ti)2O5; 3) ground state of pure and perturbed geometrically frustrated systems LiV2O4, (Y,Sc)Mn2, CePt2Sn2; and 4) magnetic properties of linear chains and 2-leg ladders in the hybrid (La,Sr,Ca)14Cu24O41. The muon spin relaxation experiments are performed at TRIUMF, magnetic susceptibility measurements at Columbia and neutron scattering studies at JAERI. This research program is interdisciplinary in nature and involves one or more graduate or postgraduate students, who receive excellent training in preparation for careers in industry, government laboratories or academia. %%% This experimental basic research project is devoted to unusual magnetic behavior in crystalline specimens of a variety of inorganic chemical compounds. The questions of interest are the local behavior of the magnetic species in the samples, and an advanced experimental method called "muon spin relaxation" is used in this work. The measurement has to be made at a special accelerator facility where the muons (mu mesons), are produced and injected into the sample of interest. The measurement reveals the magnetic field strength inside the sample at those loca tions, often near internal magnetic moments, where the muons become trapped before they undergo decay. Of interest are conditions for the formation/absence of spin freezing, the role of frustration, and effects of charge doping and magnetic dilution. In more detail, four topics and systems of interest are: 1) questions of ordering temperature and/or ordered moment size in quasi 1-d zig- zag spin chain SrCuO2 and LixV2O5; 2) charge/vacancy doping effects in 2-leg ladders Sr2(Cu,Zn)4O6, LaCuO2.5, and (Ca,Mg)(V,Ti)2O5; 3) ground state of pure and perturbed geometrically frustrated systems LiV2O4, (Y,Sc)Mn2, CePt2Sn2; and 4) magnetic properties of linear chains and 2-leg ladders in the hybrid (La,Sr,Ca)14Cu24O41.The muon spin relaxation experiments are performed at TRIUMF, magnetic susceptibility measurements at Columbia and neutron scattering studies at JAERI. The results of this research will be of importance in magnetism, and in physical theory. They may lead to new methods that can be applied in chemistry and in nanoscale electronic devices. This research program is interdisciplinary in nature and involves one or more graduate or postgraduate students, who receive excellent training in preparation for careers in industry, government laboratories or academia. ***