Here we report the magnetic properties of the layered cobalt oxide system, ${\text{Li}}_{x}{\text{CoO}}_{2}$, in the whole range of Li composition, $0\ensuremath{\le}x\ensuremath{\le}1$. Based on dc-magnetic-susceptibility data, combined with results of $^{59}\text{Co}$ nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) observations, the electronic phase diagram of ${\text{Li}}_{x}{\text{CoO}}_{2}$ has been established. As in the related material ${\text{Na}}_{x}{\text{CoO}}_{2}$, 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 $(x\ensuremath{\le}0.35)$, the antiferromagnetic spin correlations systematically increase with decreasing $x$. Nevertheless, ${\text{CoO}}_{2}$, the $x=0$ end member is a noncorrelated metal in the whole temperature range studied. In the Curie-Weiss regime $(x\ensuremath{\ge}0.40)$, 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 ${T}_{\text{t}}\ensuremath{\approx}175\text{ }\text{K}$ in samples with $x=0.50$ $(=1/2)$ and 0.67 $(=2/3)$, while only a tiny kink appears at $T\ensuremath{\approx}210\text{ }\text{K}$ in the sample with an intermediate Li composition, $x=0.60$. Thus, the phase diagram of the ${\text{Li}}_{x}{\text{CoO}}_{2}$ system is complex and the electronic properties are sensitively influenced by the Li content $(x)$.