There are a couple of textbooks I haven't seen mentioned elsewhere in this thread which I found very useful as a first year undergraduate - they are concise in

There are a couple of textbooks I haven't seen mentioned elsewhere in this thread which I found very useful as a first year undergraduate - they are concise in style but not to the point of being too difficult to follow (it's personal preference but I found I got on much better with this style of textbook): Davenport - The Higher Arithmetic Burkill - A First Course in Mathematical Analysis (and also A Second Course in Mathematical Analysis by Burkill and Burkill) Hardy and Wright - An introduction to the theory of numbers