Can I get a summary of all my invitations?

Yes. In your home page the first panel shows "My invitations". In there each event for which you have invitations will be listed and you can click on any one to get a window that shows all invitations from others that you could accept for a particular event. Your own invitations are also listed.

For each event there is an indication of how many invites you have issued (in blue) and an indication of how many invites you could accept (in orange). These indicators are correct when you load or visit this home page but, unlike most of the rest of ManageMyMatch, do not update dynamically. So if you think the situation may have changed just hit the Refresh counters button in the panel header to get the latest counts.

In the pop-up window that shows your invitations, there are filtering options to help you get a list for a particular day or person. You can cancel any one of your invitations and accept any incoming invitation from here. You can also discard an invitation if you don't think you'll be taking it up. This clears the list up for you and lets you focus on only those invitations that you may consider.

If you've opted in as an advanced user then you'll get an even better way of reviewing all your invitations along with your bookings on a weekly basis in My invitations.