Training attendance in CRM

I have a consulting business and we offer public training sessions as well. We may have several organizations sending different participants to one of our training sessions. We would like to track the attendance to these workshops, including the ability to look at a contact and see what workshops (if any) that person has attended.

I thought using Events would work, but it appears you have to actually invite them via email and have them respond, and it does not show who actually attended the meeting - just whether they are going, not going or maybe.

What is the best way to handle this.