I answer this question based on the books that I have worked with. It would be very helpful to know if you are working on your own or if you follow a beginner’s course.
French Grammar Book for Anglophones
1) My favorite book for this level
A well written book that offers the advantage of helping you to acquire everyday vocabulary and learning more than 300 useful verbs by usage.
2) English Grammar for Students of French 7th edition (O & H Study Guides)
This may look weird. But one should acquire a good knowledge of the English grammar before attempting to learn the French one. I suggest that you read the description and you see its objectifs.
It’s a little bit old and some of the examples are archaic but still its completeness (it contains almost everything), its compactness (336 pages) and its price make it irresistible.
4) Complete French Grammar
Reasonable price and hundreds of exercices with their key.
French Grammars for FLE (Français Langue Étrangère)
I emphasize that I present only books of A1/A2 level.
1) Grammaire Progressive du Français (Débutant)
Be careful that the key to the exercices is sold independently.
2) Nouvelle Grammaire du Français
Actually, this is a rather complete grammar.
3) 500 exercices de Grammaire A1 (key included)
The whole series (A1-B2) accompanies closely Reference 2.
Of course internet offers a lot of help!
http://www.languageguide.org/french/grammar/
http://www.bonjourdefrance.co.uk/learn-french-online/grammar/choose-level
Last but not least, as already mentioned see the relevant discussion here
Recommended grammar textbook for self-study
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