There is a syllabus in the online course descriptions at http://www.maths.tcd.ie/pub/official/CoursesNow.
Some of the lecture notes are available online here:
Two scale dilation equations in L2(R), Haar example, properties of the coefficients required for solution to have othonormal translates, Fourier transform as an infinite product, property of the coefficients required for solution to have nonzero mean.
Daubechies 4 coefficient example.
Support of compactly supported solutions (if they exist), graphing compactly supported continuous solutions via values at dyadic rationals.
Construction of a basic `wavelet', support, graphing it. Orthogonality properties of the wavelet. Othonormal wavelet bases in presence of multiresolution analysis properties.
Multiresolution analysis properties imply scaling function has mean of modulus one. Converesely solutions of dilation equations in L1 as well as L2 and with nonzero mean must have the multiresolution analysis properties.
Multiresolution wavelets have mean zero. Conditions on the coefficients for affine functions to be orthogonal to the wavelet.
Definition and basic results about infinite products. Uniform convergence and M test for uniform convergence.
Infinite products relating to the Fourier transform of the solution of a two scale dialtion equation. Conditions for such products to represent L2 functions with orthonormal integere translates. Statement of the Paley-Wiener thorem on Fourier transforms of compactly supported functions and use to prove conditions for a two scale dilation equation to have a compactly supported solution.
Conditions sufficient for a two scale dilation equation to have a continuous (compactly supported) solution. Application to Daubechies wavelets.
The sheet Exercises A is available online. (It deals with choosing coefficients of a dilation equation so as to satisfy various desirable requirements.)
A sample exam paper is also available.