Complete Croatian (Teach Yourself) Accompanies Book [Audiobook] [Audio CD]

The most obvious difference is between "ekavian" and "ijekavin", two different dialect named after their realisation of "e".
In Ekavian:
milk = mleko, river = reka, village = selo
In Ijekavian:
milk = mlijeko, river = rijeka, village = selo
In other words, not all "e"s are "ije" in Ijekavian but you get the picture.
Now, all Croats, all Bosniaks and all Montenegrins use Ijekavian. So do many Serbs. The majority of the Serbs use Ekavian, though.
In other words, all Ekavian-speakers are Serbs but not all Serbs are Ekavian-speakers and all Croats are Ijekavian-speakers but not all Ijekavian-speakers are Croats.

Another difference is the vocabulary. Croats are Catholics, Bosniaks are Moslems and Montenegrins and Serbs are Orthodox. Another big difference is that Serbia and Bosnia first came under the influence of Greece and later were part of the Turkish Empire for hundreds of years. Croatia first came under the influence of Italy and later was part of the Austrian empire for hundreds of years. Naturally this has left its traces. Many religious words in Serbian are Greek, in Bosnian they're Turkish/Arab and in Croatian they're Latin.
Apart from the religious vocabulary there are some other words that differ. Croatia has one set of words whereas the others have another set. In short, the picture looks like this:

Croatian: Ijekavian, religious vocabulary based on Latin, Croatian-set.
Serbian: Ekavian (mostly), religious vocabulary based on Greek, Serbian-set.
Bosnian: Ijekavian, religious vocabulary based on Turkish, Serbiat-set.
Montenegrin: Ijekavian, religious vocabulary based on Greek, Serbian-set.

Just keep in mind that there are differences but that people understand each others. I've learned Croatian but Serbs have expressed delight over how well I speak Serbian...

b. Teach Yourself Croatian
The development of courses in Croatian and Serbian is rather interesting. Up to the early 1980s most Serbo-Croatian courses were based on the Serbian variety because that was the language spoken in the capital. Then came the "tourist invasion" and since the tourist areas were almost exclusively in Croatia almost all courses published in 1980-1992 were in the Croatian variety. Now, those courses are often republised under the name of "Croatian". In fact, Teach Yourself Croatian is exactly the same books as the old Teach Yourself Serbo-Croat. This means that Serbian has the upper hand in courses at the moment, because now that there is a need for courses in the language publishers go for completely new courses. I guess that within five years we'll see new courses appearing in Croatian...

Comparing Teach Yourself Croatin to Teach Yourself Serbian, this one is substantially shorter and does not contain as much information. It is not a bad course but I wonder why they didn't make it as comprehensive as Teach Yourself Serbian. Both courses have the same authors and they were published at the same time, yet this one is only 2/3 of the other. Obviously that means that this course doesn't take the beginner as far as Teach Yourself Serbian does.

If you've read my other reviews of courses you will know that I consider most Teach Yourself courses too short. Teach Yourself Croatian suffers from the same problem, unlike Teach Yourself Serbian.