Bosnian, Croatian, Serbian, a Textbook With Exercises and Basic Grammar, 2nd Edition by Ronelle Alexander, Ellen Elias-Bursac (z-lib.org)
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I've worked with this one quite a while til i had to stop learning, was very useful for me, as my family speaks serbocroatian. It's available on z-library
This is sort of an ongoing project. I'm building the courses over on memrise.com so that once I'm done they'll be free to anyone that wants to use them.
There are actually two courses right now. There's this one for grammar:
https://www.memrise.com/course/1182652/serbian-mastercourse/
and this one for vocabulary:
https://www.memrise.com/course/1423667/serbian-vocabulary-booster/
Neither of these courses are finished and if you want to help I'd really appreciate it if you'd check in every couple of weeks to read a couple of phrases. Even if you're reading phrases that already have a recording, it's super useful to hear a variety of voices and accents.
Anyway, if you're interested in helping you'll have to make an account at memrise.com, if you don't already have one, and then you can message me and I'll make you a contributor. From there recording is pretty simple.
It took me about 6 months (although this was starting from scratch so it's including vocab etc). So you could do it very fast if you just do it consistently and really practice.
Literally all I did was follow a text book and do all the exercises in it and double check my answers with my girlfriend.
-For a free book
I still make the odd mistake here and there of course but I have the opposite problem to you, my padeži and grammar is great so people here assume I am fluent and the proceed to speak as fast as possible with words I don't know so I completely lose them XD
Alternatively you could try get lessons on Italki or Belgrade Language school(They're very expensive but very good).
Срећно бре!
Hi! My name is Nikola. I am Serbian language and literature student and I tutor Serbian as a foreign language on Preply. You can contact me on this site if you want to discuss more about the lessons! :)
The Assimil Serbo-Croate Sans Peine which is no longer produced is probably my favorite audio lesson. They start out slow and build up speed over time. Although it very quickly starts out with short sentences in lesson 2. I also found https://www.amazon.com/Colloquial-Serbian-Complete-Course-Beginners/dp/0415348927 to be pretty good.
For me, the most helpful tool has been https://www.hr4eu.hr, although it teaches Croatian. The page has plenty of exercises for grammar and vocabulary, and there are even written assignments that they check for you. Just keep in mind the differences between Serbian and Croatian.
If you're into textbooks, this book is said to be very useful: https://www.amazon.com/Bosnian-Croatian-Serbian-Textbook-Exercises/dp/0299236544
Yes, this is a great book. I've used it too. I would also recommend this one: https://www.amazon.de/Colloquial-Serbian-Complete-Course-Beginners/dp/0415348927 it includes a CD to go along with the material.
OP, you have a native speaker close to you at all times, all you need is a good textbook, patience and some hard work. Do not waste your money on those silly courses, just study the grammar and vocabulary from good textbooks and use it when speaking Serbian to your girl.