For the most recently, I need some info about topology, here I collect some introductions to William Thurston.

*[From his home page]*

Bill Thurston is a topologist, though his work impinges on many other areas of mathematics. He has discovered unexpected links between topology, hyperbolic geometry, and complex analysis.

Highlights of his career include his classification of foliations of codimension greater than one, his classification of surface automorphisms, his hyperbolization theorem in three-dimensional topology, and the theories of automatic groups and confoliations. Thurston has also made fundamental contributions to the theory of symplectic and contact manifolds, dynamics of surface diffeomorphisms, and the combinatorics of rational maps.

His current research includes random 3-manifolds and relations of knot theory to computational complexity. His main interest remains his geometrization conjecture, a far-reaching proposed generalization of his hyperpolization theorem.

- the home page at cornell university: http://www.math.cornell.edu/m/People/Faculty/thurston
- Wikipedia: http://en.wikipedia.org/wiki/William_Thurston
- terrence tao: http://terrytao.wordpress.com/2012/08/22/bill-thurston/
- outside in: http://www.youtube.com/watch?v=wO61D9x6lNY
- The Mystery of 3-Manifolds: http://www.youtube.com/watch?v=4jdmkUQDWtQ