Here, particularly I'm looking for a book which starts with set theory and constructs real numbers on that basis (it should include Dedekind cut). Other than Landau's book.
Edit: Thank you all in comments for your suggestions. I found this book 'From natural numbers to quaternions' by Kramer and Pippich (thought bit advanced atleast for me but very readable), Elementary Set theory by Enderton (Thanks to Asaf Karagila), Goldrei's book is also really good (Thanks to palmpo). Last two books I mentioned do both jobs of constructing numbers and introducing set theory really well.