A. Baker, Transcendental number theory, Cambridge 1975.
S. Lang, Fundamentals of diophantine geometry, Springer 1983.
R.C. Mason, Diophantine equations over function fields, LMS Lecture Notes 96, Cambridge 1984.
P. Vojta, Diophantine approximations and value-distribution theory, Lecture Notes 1239, Springer 1987.
TTAA = Transcendence theory: advances and applications (eds. A. Baker and D.W. Masser), Academic Press, London 1977.
DATT = Diophantine approximation and transcendence theory (ed. G. Wustholz), Lecture Notes 1290, Springer 1987.
NATT = New advances in transcendence theory (ed. A. Baker), Cambridge 1988.
MFFLT = Modular forms and Fermat's Last Theorem (eds. G. Cornell, J.H. Silverman and G. Stevens), Springer 1997.
A. Baker, The theory of linear forms in logarithms, TTAA (pp.1-27).
A. Baker and G. Wustholz, Logarithmic forms and group varieties, J. reine angew. Math. 442 (1993), 19-62.
E. Bombieri and J. Vaaler, On Siegel's lemma, Invent. Math. 73 (1983), 11-32.
G. Frey, On ternary equations of Fermat type and relations with elliptic curves, MFFLT (pp.527-548).
P. Philippon and M. Waldschmidt, Lower bounds for linear forms in logarithms, NATT (pp.280-312).
A.J. van der Poorten, Linear forms in logarithms in the p-adic case, TTAA (pp.29-57).
C.L. Stewart and R. Tijdeman, On the Oesterle-Masser conjecture, Monatshefte Math. 102 (1986), 251-257.
C.L. Stewart and K. Yu, On the abc-conjecture, Math. Ann. 291 (1991), 225-230.
W.W. Stothers, Polynomial identities and Hauptmoduln, Quarterly J. Math. Oxford 32 (1981), 349-370.
G. Wustholz, A new approach to Baker's Theorem on linear forms in logarithms I and II, DATT (pp.189-211); and III, NATT (pp.399-410).
K. Yu, Linear forms in logarithms in the p-adic case, NATT (pp.411-434).
K. Yu, P-adic logarithmic forms and group varieties I, to appear in J. reine angew Math.
But clearly no students can be expected to start studying all of these. I suggest the following subset as material to look at before the lectures:
Baker's book (Chapter 2).
Mason's book (Chapter 1).