I would combine these two sentences:
My timetable for lessons and lectures for the next academic year is for Monday's and Friday's. So, I would be available for any other days of the week, including Saturdays.
I'm not 100% sure, but I think your use of the word initiated at the beginning might be incorrect...you might want to check for yourself with someone more knowledgeable, though.
that might be on offer within your office.
The above sounds strange to me. I would consider changing to "anything your office has to offer", which is also more reader-focused.
Finally, I would consider using a business letter format rather than the good old "dear so-and-so," format. If you stick with this, make sure you put a comma after "Kind regards".
Overall, very good, though, I think. I like the strong sentences. :)
Hope we catch everything for you ;)