Learn Italian: Spero di poter migliorare la mia autostima. - I hope to be able to improve my self-esteem.

The verb sperare (to hope) normally requires the subjunctive mood when you are hoping for someone else to do something, like spero che tu possa. However, when the subject is the same for both actions (I hope that I can), Italian drops the che plus subjunctive and uses di plus the infinitive verb instead.

Why are there two infinitive verbs in a row here, poter and migliorare?

Potere is a modal verb meaning to be able to. Modal verbs are always followed directly by another verb in the infinitive. Since the grammar of this sentence forces potere into the infinitive to become poter, the second verb migliorare simply attaches right after it as usual.

Why is the word poter missing its final -e?

In Italian, infinitive verbs ending in -re (like potere, avere, or volere) frequently drop the final -e when they are followed immediately by another infinitive. It makes the sentence flow better and is very common before other verbs.

Why do we need the article la before mia autostima?