If you can, read all of Dante's Inferno. If you are pressed for time, however, make sure you read the following excerpts. Following the cantos & lines you should read are the ideas on which you should focus.

III. 1-9
Hellgate; the Oppurtunists; contrapasso; the Acheron and Charon

IV. 13-63, 79-105, 145-151
Limbo; the Harrowing of Hell; pagan philosophers and warriors

V. 1-24
Minos

VI. 7-27, 94-111
Gluttons; Cerberus; pain worse after Judgment Day

VII. 100-126
The Angry and the Sullen

X. 94-108
See past and future, not present

XI. 16-90
Virgil explains Lower Hell's structure

XII. 52-60, 73-75, 97-132
The Violent against Others; Centaurs ; the River of Blood

XIII. 1-15, 22-39, 85-108
The Wood of Suicides

XIV. 4-42, 76-84, 94-120
Burning sand; sinners lie, crouch, wander; rain of fire; the Old Man of Crete; the Rivers of Hell

XVIII. 1-39, 100-126
Malebolge described; panders and seducers; flatterers

XX. 1-30
Fortune tellers with bodies twisted

XXI-XXII
Pitch; Malebranche devils; grafters; continual fraud

XXIII. 58-72, 109-126
Hypocrites; Capaneus crucified

XXIV. 79-139
Thieves; serpents; Vanni Fucci

XXV. 1-144
Vanni Fucci; Cacus the centaur; metamorphoses described

XXVIII. 1-6, 19-42, 112-142
Schismatics; Mahomet; Ali; Bertran de Born

XXIX. 37-51, 67-84
Falsifiers; leprous sores

XXX. 22-33, 46-63, 73-75
Insane sinners; Master Adamo's dropsy

XXXII. 1-15, 22-39, 73-111, 124-139
Invocation to Muses; frozen in ice; Dante kicks and torments Bocca; Dante sees one sinner eating another

XXXIII. 1-78, 91-150
Ugolino's story; tears freeze; wind; Dante tricks Friar Alberigo

XXXIV. 1-75, 97-99, 119-139
Sinners frozen; Lucifer; Dante and Virgil climb down Lucifer; Dante and Virgil stop in a cavern; Lucifer's fall; Purgatory; Dante and Virgil leave Hell