The subjunctive is used after verbs expressing hope, wish, desire, command or doubt such as sperare - to hope, desiderare - to desire, volere - to want, and dubitare - to doubt.  But verbs that express certainty or fact used in the affirmative sense (and not negative) require the indicative, such as essere sicuro - to be sure, essere certo - to be certain, and sapere - to know.  And if the subject of both verbs in the sentence is the same, use di with the infinitive instead of the subjunctive.

Dubito che loro vengano.  I doubt that they'll come.
Spero che lei vinca.  I hope that she wins.
Non so se i musei siano aperti.  I don't know if the museums are open.
So che i musei sono aperti.  I know that the museums are open.
Non credo di averlo perso.  I don't think that I lost it.

The subjunctive is also used after impersonal expressions, usually essere and an adjective or adverb, unless they state a fact.  Some common expressions are è necessario - it's necessary, è meglio - it's better, è possibile - it's possible, and è probabile - it's probable.  The indicative is used after these expressions of certainty: è certo - it's certain, è sicuro - it's sure, and è vero - it's true.

Certain conjunctions require the subjunctive as well, such as sebbene - even though, benché - although, affinché - so that, prima che - before, purché - provided that, as long as and nel caso che - in the event that.  The subjunctive is also used after a relative superlative che, and after il primo.. che, l'ultimo..che, and il solo...che.

The possessive pronouns replace a noun, and they have the same forms as the possessive adjectives.  They always require an article, unless the possessive pronoun follows the verb essere, in which case it is omitted.

Non parlo a tua madre. Parlo alla mia.  I'm not talking to your mother.  I'm talking to mine.
Questa macchina è mia.  This car is mine.

The historical past or past absolute is used to indicate a completed action, and is used mainly in writing and rarely in speech.  It is not a compound tense, and is formed by dropping the regular stems of the verbs and adding these endings:

Avere and essere and many other verbs are irregular in the historical past:

The following verbs are irregular only in the io, lui/lei and loro forms.  The verbs are all either -ere or -ire verbs, so use the irregular stem for these three forms and add these endings: -i, -e, -ero.  Use the regular stem and regular endings for the other three forms.

The past perfect of the historical past is formed the same way as the past perfect of the indicative.  Just add the past participle to the historical past of avere or essere.