Another bit of my forgotten past comes flooding back … My sister and I used to share these things; it was one of two areas where we pooled our resources (these books, and Lego). We had quite a little stockpile of them at one point. I have no idea what became of them …
Slim like issue 5020 - How and Why - Ballet. 
I think it was just “Life Science Library” not “Time/Life” etc, see here. We had the full set of these when I was a kid. They vastly stimulated my interest in science of any sort, but particularly Astronomy, and I was positive I wanted to be an astronomer when I grew up. It would be amusing to see the volume The Universe again, and see how badly and in what ways it’s out of date.
I think I read one or two of the How and Whys, but I was obsessed with the Life Science (and to a lesser extent, Life Nature) Library. I read every single one of them as a kid, starting with Health and Disease when I was probably in second or third grade. It had this rad cover with a syringe and flies and grain. In the inlay of each book there was an explanation of what the cover represented. Very cool. They were already showing their age in the late 70s (I remember laughing at the spacesuits in Man and Space).
squeegee, The Universe was actually a volume in the Life Nature Library. The font on the cover was a little different, skinnier and taller.
We had a son 5 months ago today and just the other evening out of nowhere came flooding back memories of how these books used to ignite my imagination. I was wondering whether they were still around in updated form for him! They look so dated now but they were my bible too, and I spent hours reading and re-reading them over and over. Judging by the responses here I can unequivocally say Dopers really are MY PEOPLE!!
I remember that I was given the Civil War book to read on my first airplane flight, while my sister was given the Florence Nightingale.