Rearrange README and fix typos

Author: skade

README.md

@@ -7,11 +7,14 @@ https://github.com/async-rs/async-std)
 [![Documentation](https://docs.rs/async-std/badge.svg)](https://docs.rs/async-std)
 [![chat](https://img.shields.io/discord/598880689856970762.svg?logo=discord)](https://discord.gg/JvZeVNe)
 
-This crate provices an async version of [`std`]. It provides all the interfaces you are used to, but async and ready for Rusts `async/await`-syntax.
-
-For detailed information, take a look at the [documentation][docs] and the associated [book][book].
+This crate provides an async version of [`std`]. It provides all the interfaces you are used to, but async and ready for Rusts `async/await`-syntax.
 
 [`std`]: https://doc.rust-lang.org/std/index.html
+
+## Documentation
+
+`async-std` comes with [extensive API domentation][docs] and a [book][book].
+
 [docs]: https://docs.rs/async-std
 [book]: https://book.async.rs