There are 32 boroughs in London (thirtythree with the City of London which is the number 1 but is not a London Borough, being simply a district, though historically of preminent importance, without a proper London Borough Council).
Twelve of them are named as Inner London; the remainents are defined instead as Outer London.
There are some administrative differences between the two kinds of Boroughs, though most of people think that Inners are those closer to the City of London, while the Outers should be those more far (both feature are anyway exact).
In the southern boundary we find Croydon, while the western boundaries are delimited by Hillingdon; on the extreme north we find Enfield and on the east boundaries both Bexley and Havering.
It's useful to know that the boroughs are local authorities, each one of them administrated by its own London Borough Council, elected every four years, which is responsible for local services, many of them as important as local education system, housing and libraries.
There is also the Greater London Authority which is responsible for wider services like fire, highways, transports and strategic plannings.