Let $X$ be an algebraic curve over an algebraically closed field $k$ of characteristic $p\geq 0$. When $p=0$, the algebraic fundamental group $\pi_{1}(X)$ of $X$ introduced by A. Grothendieck is completely determined by its topological fundamental group (i.e., the topological fundamental group of the Riemann surface determined by $X$). Obviously, the isomorphism class of $X$ cannot be determined by the isomorphism class of $\pi_{1}(X)$.

On the other hand, when $p>0$, the situation is quite different from that in characteristic $0$. Almost 26 years ago, Prof. A. Tamagawa showed evidence for very strong anabelian phenomena for curves over algebraically closed fields of positive characteristics. This means that the isomorphism class of $X$ can be possibly determined by the isomorphism class of $\pi_{1}(X)$. This kind of anabelian phenomenon was deeply studied by Professors F. Pop, M. Raynaud, M. Sa\"idi, Tamagawa, and the speaker over the past 26 years. In this talk, I will explain some philosophy concerning fundamental groups of curves and anabelian geometry in positive characteristics from the viewpoint of moduli spaces of fundamental groups which were introduced by the speaker. This talk will be given in Japanese.