>>>>>Hi,
>>>>>
>>>>>I downloaded and installed SQL Server 2008 R2 Express on the computer which didn't have any other version of SQL Server. The installation went through without errors. Now when I start SSMS the Window Connect to Server shows the server name as (local). And Authentication is Windows. When I click on Connect I get error.
>>>>>

>>>>>A network-related or instance specific error occurred while establishing a connection.  The serve was not found or was not accessible... 
>>>>>

>>>>>When I click on the pull-down list of the Server name and then on click on "Browse for more" no server names appear.
>>>>>What step do I need to make the server accessible?
>>>>>TIA.
>>>>
>>>>Run SQL Browser.
>>>>Are you sure you added current user as administrator when you installed SQL Server?
>>>>Are Service run?
>>>
>>>I opened the SQL Server Configuration Manager. The SQLEXPRESS is running. But the SQL Server Browser is stopped. And I don't have the option to start it (when right-mouse click).
>>
>>Use the Services app from Administrative Tools to set the properties for the SQL Browser service.
>
>Success! Now when I started the SQL Server Browser and enter the name not as local but as COMPUTERNAME\SQLEXPRESS I get into the SQL Server.
>Thank you all very much.

:-)
SQL Server Browser is just for that - to find named instances of the SQL Server.