بعد أن أعود إلى البيت، أقرأ بريدا من الشركة.

Arabic often leaves the subject pronoun unstated because the verb already shows it.

• أعود = I return / I go back
• أقرأ = I read

So you do not need أنا unless you want emphasis. If you did add it, it would usually sound emphatic: أنا أقرأ = I read.

بعد أن means after when it introduces a whole clause.

So:

• بعد أن أعود إلى البيت = after I return home

It is literally something like after that I return home, but in natural English we simply say after I return home.

You may also see other ways to express this idea, such as بعدما or a verbal noun construction, but بعد أن is a very standard and clear choice.

In Arabic, the imperfect verb form is often used after time expressions like بعد أن to talk about an action that is future relative to another action, or part of a repeated sequence.

So أعود here does not mean only I am returning. In context it means:

• after I return
• or after I come back

Also, after أن, the verb is grammatically in the subjunctive. In fully vowelled Arabic, this would be أعودَ. In normal unvowelled writing, that difference is usually not shown.

A fully vowelled version would be:

بَعْدَ أَنْ أَعُودَ إِلَى الْبَيْتِ، أَقْرَأُ بَرِيدًا مِنَ الشَّرِكَةِ.

Some useful details:

• بعدَ: final -a sound
• أعودَ: subjunctive after أن
• البيتِ: genitive after إلى
• أقرأُ: indicative
• بريدًا: accusative because it is the direct object
• الشركةِ: genitive after من

In everyday writing, these endings are usually omitted.

The verb عاد in Modern Standard Arabic commonly uses إلى to mean return to a place.

So:

• عاد إلى البيت = he returned home / to the house
• أعود إلى البيت = I return home

English often says simply return home without a preposition, but Arabic usually keeps the preposition here.

Yes, البيت literally means the house, but it is also commonly used to mean home in context.

So إلى البيت often naturally means home rather than specifically to the house as a physical building.

Arabic can also use المنزل, but البيت is very common and natural.

The plain imperfect أقرأ can express more than one idea, depending on context:

• a habitual action: After I return home, I read mail from the company
• a future action in a sequence: After I return home, I’ll read mail from the company

Because the time relationship is already clear from بعد أن, Arabic does not always need سـ or سوف.

If you want to make the future meaning more explicit, سأقرأ is possible, but أقرأ is perfectly natural here.

Here بريدا is an indefinite direct object, so it means something like:

• some mail
• a letter
• a message
• possibly an email, depending on context

In fully vowelled writing it would be بريدًا. The -an ending is because it is the direct object of أقرأ.

If you said البريد, that would mean the mail or the post, referring to something definite or already known.

بريد can mean mail/post in a general sense, and in modern usage it can also refer to email if the context supports that.

So this sentence could mean:

• mail from the company
• a message from the company
• possibly an email from the company

If you want to say email very explicitly, Arabic often uses بريد إلكتروني.

It describes بريدًا.

So the meaning is:

• mail from the company
• not I read from the company

Here من shows source or origin:

• من الشركة = from the company

So the structure is:

• أقرأ = I read
• بريدًا = mail / a message
• من الشركة = from the company

Together: I read mail from the company.