Suppose $M$ is a subset of a Banach space $X$.
Here, page $179$, the author defined Lipschitz-free space $\mathcal{F}(M)$ to be the canonical predual of the space of Lipschitz functions Lip$(M)$, i.e. the closed linear span of the point evaluations $$\delta_M(x)(f)=f(x), x \in M$$ in Lip$(M)^*$.
Question: I don't understand the definition of the Lipschitz-free space. Can anyone give some examples so that I can understand it?