See the question. I want to see the methods and classes offered by a DLLs library.
There's also the DLL export viewer if you don't have VS installed on a machine.
If the DLL is a .NET assembly you might want to take a look at Reflector for a more detailed view.
ILSpy is an open-source tool which allows you to browse an assembly's packages and classes and also to decompile code.
Another free-of-charge tool is JetBrain's dotPeek.
Outside of Visual Studio, you can use a dependency tool which is able to inspect DLL and EXE imports and exports, it integrates with the shell and is very easy to use. It comes with some Microsoft SDKs. If you want to avoid the hassle of downloading and installing SDK just because of this, easy download links for all 32b/64b platforms are available at http://www.dependencywalker.com/
Microsoft documentation (no download) is available at MicroSoft Technet
Similar functionality is also available in SysInternals Process Explorer - best suited when inspecting running processes.
There's a dependency tracker tool that comes with the Windows SDK (formerly the Platform SDK), it's got a reasonable GUI for looking inside executables and DLL's.
There are also some command line tools that you can use to see inside of dll's, dumpbin in particular - check the MSDN help in visual studio for more information. You can run these tools from the command prompt in the Visual Studio start menu folder.
This is exactly what the Object Browser is for.