These lecture notes were prepared by Vitali Liskevich with minor adjustments by Vitaly Moroz, Spyros Dendrinos, Jens Marklof and Ivor McGillivray.

Chapter: 1, 2, 3, 4, 5, 6, 7.

Week 1 - set 10/10/2011- Exercises 1: Q5, Q8, Q10
Week 2 - set 17/10/2011- Exercises 1: Q13; Exercises 2: Q1, Q2
Week 3 - set 24/10/2011- Exercises 2: Q4, Q5, Q7
Week 4 - set 31/10/2011- Exercises 3: Q1, Q5, Q6, Q7
Week 5 - set 07/11/2011- Exercises 4: Q4, Q8, Q9, Q10
Week 6 - set 14/11/2011- Exercises 5: Q1, Q5 a), b), Q6
Week 7 - set 21/11/2011- Exercises 6: Q1, Q5 a), b), Q8, Q14
Week 8 - set 28/11/2011- Exercises 7: Q1, Q2, Q3
Week 9 - set 05/12/2011- Exercises 7: Q7, Q9, Q10
Week 10 - set 12/12/2011- Exercises 8: Q1, Q2, Q3
Week 11 - set 16/01/2012- Exercises 8: Q4, Q7, Q8 except e), g)
Week 12 - set 23/01/2012- Exercises 8: Q5, Q6; Exercises 9: Q1
Week 13 - set 30/01/2012- Exercises 9: Q2, Q3, Q4
Week 14 - set 06/02/2012- Exercises 9: Q5; Exercises 10: Q2
Week 15 - set 13/02/2012- Exercises 10: Q3, Q4, Q5
Week 16 - set 20/02/2012- Exercises 11: Q1, Q2, Q3
Week 17 - set 27/02/2012- Exercises 11: Q5, Q6, Q7
Week 18 - set 05/03/2012- Exercises 12: Q1, Q4, Q5
Week 19 - set 12/03/2012- Exercises 12: Q8, Q9, Q12
Week 20 - set 19/03/2012- Exercises 13: Q7, Q8, Q9
Week 21 - set 23/04/2012- Exercises 13: Q11, Q12; Exercises 14, Q1
Week 22 - set 30/04/2012- Exercises 14: Q3, Q4, Q6
Week 23 - set 07/05/2012- Exercises 15: Q2, Q5; Exercises 16: Q6

Gowers' weblog
A brief history of mathematics

R.G. Bartle and D.R. Sherbert, Introduction to real analysis. John Wiley & Sons, Inc. 2000.

C.W. Clark, Eementary mathematical analysis. Wadsworth Publishers of Canada, Ltd., 1982.

J. M. Howie, Real analysis. Springer-Verlag, 2001.

S. Krantz, Real Analysis and Foundations. Second Edition. Chapman and Hall/CRC Press, 2005.

I. Stewart and D. Tall, The Foundations of Mathematics. Oxford University Press, 1977.

You can find them in Courses/Math Teaching/Exams/Past Examinations.