There are two unfortunate news here. Firstly the research is scattered around and I can't think of any definitive references that would be easy places to start. Secondly you need to be able to read some languages in order to be able to get full access to the literature. More and more is being written in English but you still find a lot of literature that's in Finnish, Russian or German. I've even seen a few papers written in Inari Saami and Komi. Those were probably exercises to develop the technical vocabulary of the languages but also probably partly linguistic showing off. I'm a bit bummed here myself for not having bothered to learn Russian.
You should look at the of the Fenno-Ugrian Society. The journal has been online for the three last issues while the series includes a lot of monographs and article compilations many of which are online as well. You might also want to look at the papers published in .
Some papers you might be interested in are: Janhunen (1982), On the structure of Proto-Uralic, Sammallahti (1988), Historical phonology of the Uralic languages, Janhunen (2007), The primary laryngeal in Uralic and beyond, Janhunen (2009), Proto-Uralic—what, where, and when?, Aikio (2012), On Finnic long vowels, Samoyed vowel sequences, and Proto-Uralic *x, Häkkinen (2012), Early contacts between Uralic and Yukaghir, Kallio (2012), The non-initial-syllable vowel reductions from Proto-Uralic to Proto-Finnic,
Remember also the on Uralic which compile a lot of diachronic stuff. And for Saamic sound history there's lecture material for the consonants () and vowels (). Both of these are from The Saami Languages - An Introduction (Sammallahti, 1998).
From the reference books I've been reading Abondolo's Uralic Languages (from Routledge's Language Family Series, 1998). It has a fair amount of information of the included languages as well as some diachronic stuff, but because of its format it can't go very deep into the subject anywhere. Other people should have experience from other reference books.
If you are interested in the Finnish sound history and willing to invest some effort in your studies, your best bet will be learning to read Finnish as it is the language of most of that literature. In that case (Lehtinen, 2007) would be a great resource. It describes the development from Proto Uralic into the Finnish dialects and is written on the level of an undergraduate university course or an informed enthusiast.
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