The text discusses five common connection errors in PostgreSQL and provides solutions for each of them. These errors include "Sorry, Too Many Clients Already", "No pg_hba.conf Entry for Host", "Connection to Server on Socket Failed: No Such File or Directory", "Connection to Server Failed: Connection Refused", and "Database 'X' Does Not Exist". The solutions involve checking server settings, adjusting connection parameters, ensuring the PostgreSQL server is running, and creating or specifying existing databases.