The nuclear magnetic susceptibility χ of liquid He3 has been studied as a function of temperature (0.07 to 4.2°K) and pressure (0.7 to 27.5 atm). it has been found that Curie's law holds above 2°K, where the experimental results showed an rms deviation of less than 1.5%. At 1.1°K the liquid is (5+/-1.5)% degenerate; no pressure dependence of χ could be detected above 1.2°K. As the temperature is reduced below 1.1°K, the product χT falls monotonically and χ tends towards the constant zero-temperature limiting value; χ increases with increasing pressure in this temperature range and values of TF**, the magnetic degeneracy temperature, as a function of pressure are given. The low-temperature results are considered in the light of the Fermi-liquid theory of Landau and its extension to finite temperatures. A plot of reduced susceptibility versus reduced temperature, of the type suggested by Goldstein, indicates that data at all pressures and temperatures may be described closely (within 3%) by a single function. Comparison of this work is made with published results from other laboratories. The spin-lattice relaxation time has also been investigated over the same pressure and temperature ranges, and lower limits for (T1)bulk at low temperatures have been deduced. An analysis of the type suggested by Low and Rorschach was applied for this purpose. The results are the first reported in the Fermi-liquid region, and at higher temperatures they are compared with data published elsewhere. Low-temperature thermometry was facilitated by measurement of the nuclear susceptibility of F19 in a calcium fluoride crystal immersed in the liquid He3.