SQL Server total memory less than target memory, lot of extra memory unallocated The situation is the following:
We have a SQL2008r2 server (64bit on 64bit Windows) with SSRS installed on it. The Max Memory is set to 6GB, the server has 12GB total memory. 

The target server memory is always more than the total server memory (for instance total: 2758MB, target: 6144MB = 6GB, which is the max memory).

My problem is that the server has 6GB free memory, but the SQL Server is not using the available space, nor SSRS, or other process. Can anyone tell me is this normal? I've found nothing regarding this topic online.
This is normal.  

Max server memory means that your server cannot use more than that amount, not that it must use that amount.  Min server memory doesn't mean it must use that amount, either;  it means that once the server uses that much it doesn't surrender memory to below that amount.  Basically, SQL Server uses the amount of memory it needs until it reaches the upper limit you set, and if it stops using it it might surrender part of it back unless you've set a min memory.  (However, in my experience, it's pretty memory-greedy.)

In short:  This means that you're currently not using 6GB of memory on your SQL Server.