Book on infinitely generated Abelian groups

Question

I (believe to) understand "sufficiently well" finitely generated Abelian groups. As a consequence of looking on some direct limits of such groups, I am now however faced with infinitely generated ones. I yet lack basic understanding, but I believe I might be faced with mixed ones, especially with ones involving direct sums of Lie groups and periodic ones. My intuition also tells me that I am likely facing "rather standard"/ better researched infinitely generated ones (whatever this might mean, just a feeling from what I read). Is there any good (and preferably affordable) book you can recommend? The book can presume knowledge of finitely generated Abelian groups, but should start at the basics of infinitely generated ones.