Considering SSI transactions
On top of read committed and repeatable read, PostgreSQL offers serializable (or SSI) transactions. So, in all, PostgreSQL supports three isolation levels. Note that read uncommitted (which still happens to be the default in some commercial databases) is not supported: if you try to start a read uncommitted transaction, PostgreSQL will silently map to read committed. However, back to serializable.
The idea behind serializable is simple; if a transaction is known to work correctly if there is only a single user, it will also work in the case of concurrency if this isolation level is chosen. However, users have to be prepared; transactions may fail (by design) and error-out. In addition to that, a performance penalty has to be paid.
If you want to know more about this isolation level, consider checking out https://wiki.postgresql.org/wiki/Serializable.