An Essential Grammar is an accessible, up-to-date Polish Grammar for English speakers. Organised in ten sections, this book provides in-depth coverage of all grammar elements. Refreshingly jargon-free, it explains genders, noun types, cases and case requirements of prepositions supplemented with authentic examples.
The book could, arguably, have given more examples for how/when to use various case endings, but it otherwise very much lives up to its title and it is an excellent companion tool for learning Polish. I think it would be very, very difficult to learn Polish just with this book, but in conjunction with other learning materials (including DuoLingo or Babble), I think it is an invaluable tool.
Although this book has a good pronunciation guide, you won't learn how to speak/hear Polish this way (but why would you ever expect to from a book, right?).