1. Present tense and past tense
Modal Auxiliaries
Present tense and past tense

2. Present Tense Modal Auxiliaries Sentence Structure
Basic sentence structure:
Ich lese ein Buch.
Subject verb object
In modal sentences the modal takes the place of the verb. The verb moves to the end of the sentence in the infinitive form.
Ich möchte ein Buch lesen
Subject modal object verb (in infinitive)

3. Negating Modals
If there is a verb in the sentence the nicht moves after the modal
Sie möchte nach Deutschland fahren.
Sie möchte nicht nach Deutschland fahren.
If there is no verb in the sentence the nicht moves to the end of the sentence.
Er mag das Buch.
Er mag das Buch nicht.

4. Modal Auxiliaries ( sometimes called helping verbs) help to set the mood of a particular sentence in which they occur. Look at the English sentence and see how each modal auxiliary changes the meaning.
Anne mag ein Buch lesen.
Anne likes to read a book.
Rainer möchte ein Buch lesen.
Rainer would like to read a book .
Boris muss ein Buch lesen.
Boris must read a book.
Julia will ein Buch lesen.
Julia wants to read a book.

5. Useful Tips
When using modal auxiliary , it is very important to remember that the infinitive of the main verb is placed at the end of the sentence.
The modal auxiliary appears in the position normally held by the verb.
Sometimes the main verb can be eliminated , provided that the meaning is clear by using the modal auxiliary.
Tina will in die Stadt gehen.
Tina will in die Stadt.

6. Modals to know: Mögen: to like Möchten: would like to Müssen: must, to have to Wollen: to want to Dürfen: may, to be allowed to Können: can, to be able to Sollen: should, to be supposed to

7. Conjugating modals
Only the modal is conjugated, not the verb at the end. The modal follows the same conjugating pattern as a verb. Ich mag Pizza essen. Du magst Pizza essen. Er,sie,es mag Pizza essen. Wir mögen Pizza essen. Ihr mögt Pizza essen. Sie mögen Pizza essen.

8. Past Tense of Modal Auxiliaries
Mögen: mochte
Müssen: musste
Wollen: wollte
Dürfen: durfte
Können: konnte
Sollen: sollte
The past tense forms are given in the 1st and 3rd person singular, all others need to be conjugated.

9. Please note the 1st and 3rd person singular are the same and is the base form of the past tense.
Mögen: Dürfen:
Ich mochte durfte
Du mochtest durftest
Er,sie ,es mochte durfte
Wir mochten durften
Ihr mochtet durftet
Sie mochten durften