For example say I have four fields and the following three records:
Lecture A | Location X | 10/10/2014 | 10 slides
Lecture B | Location X | 04/11/2014 | 20 slides
Lecture C | Location Y | 10/10/2014 | 15 slides
I would like to create a layout that summarises this information in three lines.
Unless you described either your setup or your goal incorrectly, then I'm not sure what exactly it is you want to summarize – you have three records, each describing a different lecture, and one of the attributes is the number of slides. Each record already is an instance (the only one) of a lecture, and simply listing them will give you three lines.
It would be different if you actually have a Lectures table (as described above) and a related child table of Slides; there you'd have 45 (10+20+15) records, which you could then summarize by their parent (lecture) record, to arrive at 3 lines (if you don't use a body part), each showing data from the parent plus a summary field for the number of slides per group (parent).
If what you actually have is the record for each of 45 slides, then you will want a subsummary part on the layout when sorted by lecture, and sorting on the lecture will give you the 3 subsummaries in a line each. By removing the BODY part from the layout, your report will be just those thre lecture lines. Pretty much what Erolst said, but noting the layout parts involved.