**Lecture 00:**Background, not lecturedSecond Order Logic (SOL) and its fragments LOGICS, (14 slides)

Slides prepared for the Vienna lectures**Lecture 01:**March 26/28Classical graph properties and graph parameters and their definability in SOL (4 hours) G-PARAMETERS, (60 slides)

Slides prepared for the Vienna lectures**Lecture 02:**March 28/April2One, two, many graph polynomials (4 hours) LANDSCAPE, (ca. 50 slides)

Lecture from my Technion course on Graph polynomials**Lecture 03:**April 2/April 4The characteristic and the matching polynomial (4 hours MATCHING, (54 slides)

Lecture from my Technion course on Graph polynomials (prepared by Ilia Averbouch, 2006)**Lecture 04:**April 7Recurrence relations for graph polynomials definable in CMSOL (1 1/2 hours) RECURRENCES, (27 slides)

Lecture given at the occasion of B. Trakhtenbrot's 85th birthday.

For the Cayley-Hamilton Theorem, see wikipedia.**Lecture 05:**April 9Intriguing graph polynomials: Why is the chromatic polynomial a polynomial? (1 1/2 hours) INTRIGUING, (51 slides)

Lecture given at FoCM (Budapest, 2011)**Lecture 06:**April 9Comparing graph polynomials (1 hour) COMPARING, (31 slides)

Lecture from my Technion course on Graph polynomials**Lecture 07:**April 30On connection matrices and their use in showing non-definability (4 hours) CONNECTION, (80 slides)

Lectures from the FMT-2012 meeting in Les Houches, France (May 2012)

Lecture given by Dr. T. Kotek (his version to be posted)**Lecture 08-09:**May 07-09On the location of roots of graph polynomials. ROOTS, (53 slides)

Lecture also given in Budapest on April 29, 2014. ELTE

### Additional slides

**Lecture XX:**To be given later in the courseGraph polynomials in Physics and Chemistry (2 hours) CHEMISTRY, (38 slides)

Lecture from my Technion course on Graph polynomials (prepared by Bella Dubrov, 2006)