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+# Math4202 Topology II (Lecture 1)
+
+## Topology of manifolds
+
+### Fundamental groups
+
+Use fundamental group as invariant for topological spaces up to homeomorphism (exists bijective and continuous map with continuous inverse) / homotopy equivalence.
+
+Classifying two dimensional surfaces.
+
+- Sphere
+- Torus
+- $\mathbb{R}P^2$
+
+## Quotient spaces
+
+Let $X$ be a topological space and $f:X\to Y$ is a continuous, surjective map. WIth the property that $U\subset Y$ is open if and only if $f^{-1}(U)$ is open in $X$, we say $f$ is a quotient map and $Y$ is a quotient space.