The New Penguin Russian Course is probably my favourite and most frequently used book for learning Russian. Its suitable for complete beginners, although you will want to supplement it with other methods of learning as well. The book explains grammar very well and the learning curve is fairly gentle. Many chapters contain extra, more detailed material and grammar for more advanced students.
Recommended for beginners and intermediate Russian language students.
Every language student needs a dictionary and the Oxford Mini Dictionary is perfect for use both in the classroom and whilst on holiday in Russia. Whilst you can get a Russian dictionary on your smartphone these days, you still can’t beat a pocket dictionary for use of use.
Learn Russian by Ian Press is another great book for learning Russian. This book is a little heavier on grammar than The New Penguin Russian Course but it’s still very useful and perfect for those trying to master grammar.