The book is available at Hathi Trust (I have not checked for other online sources).
I. The Discovery of Achilles
II. The Quarrel
III. Odysseus Among the Soldiers
IV. The Challenge of Paris
V. Seen From the Trojan Wall
VI. The Combat
VII. The Breaking of the Truce
VIII. The Meeting of Glaucus and Diomedes
IX. Hector and Andromache
X. The Sacrifice
XI. The Combat of Hector and Ajax
XII. Hector Victorious
XIII. A Visit to Achilles
XIV. The Horses of Rhesus
XV. Hector at the Gate
XVI. Hector at the Ships
XVII. Patroclus
XVIII. The Struggle for the Body of Patroclus
XIX. Achilles Over the Trench
XX. The Shield
XXI. Achilles to the Front
XXII. Achilles Baffled
XXIII. Achilles and the River
XXIV. Hector Meets His Fate
XXV. Andromache
XXVI. The Funeral of Patroclus
XXVII. Priam and Achilles
XXVIII. The Return of Priam
XXIX. Achilles Meets His Destiny
XXX. The End of the War
