To begin with you would need a Form for the initiator to populate their personal details and which option that they would like to attend, you could add an approval step in this process so that an internal member could confirm that there are seats available on the course and if approved an email can then be sent to the initiator and then call a Workflow to update back end/internal tables.

As for your business process you would then need Forms to make a call to a Workflow which would retrieve the Business Process Variables from the form after the approval stage, insert into a SQL table of registered parties and maybe some token calculator after a lookup to update the number of attendees in a separate course table in SQL which could update the number of attendees. This would retrieve the current number of attendees then add 1 to that value and write back to the specific column.