Here is a list of the grammar taught in second semester at the University of Iceland’s Icelandic for Foreigners Bachelor program. If you want me to teach something that’s on here or is on the first semester list, just let me know.

Declining irregular nouns
Sá – used as a back-reference in a sentence, also meaning “the one” (who took the book was…)
Weak declension of adjectives
About nouns that can’t be counted normally (like milk, coffee – you can’t say “two coffees” or “two milks” but you can say “two cups of coffee/milk”)
Impersonal verbs
When to use which case when using numbers and addresses
When and how to use það
Topicalization
Sjálfur and when to use it
Sem and how to use it when putting two sentences together.
Allur and enginn, how to use them
Negative words (ekki, aldrei, varla, hvergi, hvorki) used with neinn, nokkur
Einhver and eitthvað usage
Sumir and báðir usage
Hvorugur, annar usage
Reciprocity (reflexive verb forms)
Middle voice verbs (miðmyndarsagnir)
Subjunctive (Viðtengingarháttur)
Past-tense
Passive voice
Past participles

Comparatives (miðstig) and superlatives (efstastig)

Miðstig (mst.) changes the word’s ending to -(a)ri if the word is masculine or feminine, and to -(a)ra if the word is neuter. If the word is plural it changes to -(a)ri.
Efstastig (est.) changes the word’s ending to -(a)st.

You put this changed ending after the stem. If using the superlative, then tack on the original ending of the word too. The notes below are taken straight from the course, with just my translations added.

gulur – yellow
gul-ari – yellower
gul-ast-ur – yellowest

Bókin mín er gul-ari en þín (my book is yellower than yours)
Húsið mitt er gul-ara en þitt (my house is yellower than yours)
Pennarnir mínir eru gul-ari en þínir (my pens are yellower than yours)
Þessi bíll er gul-ast-ur. (this car is the yellowest)
Þessir litir eru gul-ast-ir. (these colours are the yellowest)
Bókin mín er gul-ust (My book is the yellowest – Remember the a-víxl!)
Húsið mitt er gul-ast (My house is the yellowest)

Common exceptions and how they decline:
gamall, eldri, elstur (old, older, oldest/eldest)
góður, betri, bestur (good, better, best)
lítill, minni, minnstur (little, less, least or small, smaller, smallest)
mikill, meiri, mestur (much, more, most)
vondur, verri, verstur (bad, worse, worst)