Universes are two types
1) Simple Universe and
2) Complex Universe

There are two types of Universes -
1. Simple
2. Linked

There are 3 types of universes:
1) shared: Available to multiple users
2) personal:Belongs to user who created it,others cannot 
use it.
3) Secured:These are centeralized and any one can use and 
used for deploy business objects reports.

Simple and Complex are the two types of Universes. 
Shared, Personal and Secured are Universe Connection types.

Thanks,
Naresh.

Types of Universes:
1) Simple
2) Complex

Shared, Personal and Secured are not universe types.
They are universe connection types.

Derived Universe, Linked Universe and Core Universe are the 
Types of Universe.

simple and complex(linked universe)

There are two types of universes : Generic and Non Generic. 

Genric Universe: Where users can create Adhoc Reporting 
(Usually it is not complex and does not have Derived Tables)

Non-Generic: This type of universe has canned reports 
created out of this universe and usually this can be termed 
as complex universe, since users do not create their own 
reports from this type of universe.