Here we report the magnetic properties of the layered cobalt oxide system, LixCoO2, in the whole range of Li composition, 0≤x≤1. Based on dc-magnetic-susceptibility data, combined with results of 59Co nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) observations, the electronic phase diagram of LixCoO2 has been established. As in the related material NaxCoO2, a magnetic critical point is found to exist between x=0.35 and 0.40, which separates the Pauli-paramagnetic and Curie-Weiss metals. In the Pauli-paramagnetic regime (x≤0.35), the antiferromagnetic spin correlations systematically increase with decreasing x. Nevertheless, CoO2, the x=0 end member is a noncorrelated metal in the whole temperature range studied. In the Curie-Weiss regime (x≥0.40), on the other hand, various phase transitions are observed. For x=0.40, a susceptibility hump is seen at 30 K, suggesting the onset of static antiferromagnetic order. A magnetic jump, which is likely to be triggered by charge ordering, is clearly observed at Tt≈175 K in samples with x=0.50 (=1/2) and 0.67 (=2/3), while only a tiny kink appears at T≈210 K in the sample with an intermediate Li composition, x=0.60. Thus, the phase diagram of the LixCoO2 system is complex and the electronic properties are sensitively influenced by the Li content (x).