What is Michaelis constant, maximum rate, catalytic and specificity constants?

For the mechanism $\mathrm{E + S \rightleftharpoons ES \to E + P}$ ($k_1$, $k_{-1}$, $k_2$) at total enzyme concentration $[\mathrm E]_0$, the catalytic constant is $k_{\mathrm{cat}} = k_2$, the maximum rate is $V_{\max} = k_{\mathrm{cat}}[\mathrm E]_0$, the Michaelis constant is $K_M = (k_{-1} + k_2)/k_1$, and the specificity constant is $k_{\mathrm{cat}}/K_M$.