How should I correctly use “sollen”?

Question

What do these two sentences mean?

Ich soll das Buch lesen.

Ich sollte das Buch lesen.

I have mostly seen "should" translated as "sollte", but that seems to be past tense. The first one would be "I should read the book." and the second one "I should have read the book."

I believe this is incorrect, however. What is the proper use of this verb? What is the difference between "ich soll", "ich solle", and "ich sollte"?

Answer 1

Ich soll das Buch lesen

means "I'm supposed to read this book", like when a teacher assigns you the book to read as your homework.

Ich sollte das Buch lesen.

can mean both "I should read this book", as in "all things considered, I really should...", and "I was supposed to read this book", as in "What was my homework for today? Oh, right, I was supposed to..."

The form "ich solle" is subjunctive, which means you basically only need it to make reported speech sound formal:

"Hast Du Peter nach den Deutsch-Hausaufgaben gefragt?" -- "Ja, er hat gesagt, ich solle das Buch lesen."

"Did you ask Peter about your German homework?" -- "Yes, he said I was supposed to read this book."

In everyday speech, however,

"Hast Du Peter nach den Deutsch-Hausaufgaben gefragt?" -- "Ja, er hat gesagt, ich soll das Buch lesen."

is just fine.