Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh

Adhan and Iqama are Fardh Kifayah (collective duty). Adhan is intended to announce the arrival of time for Salah; while Iqamah meant to inform the start of Salah (in the congregation).  So it behooves the Muslim community in every city or village to ensure that these symbols are instituted and practiced.

If, however, a person is praying by himself, it is also recommended for him to offer adhan and iqama; he may simply read the Iqamah if adhan has already been called in the city.

The prayer, however, is still valid if a person forgets or omits adhan and iqama. Since both of them are excellent forms of dhikr, one may do well to call adhan and iqamah before starting the salah.

Here is a tradition from the Prophet which recommends even a loner praying in solitude to  call adhan:

Imam Malik and others report on the authority of Abu Sa`id al-Khudri: The Prophet told Abu Sa`sa`ah: I see you love to spend time in the desert tending the sheep. So, if you are in the desert or with your sheep, and you want to call adhan, make sure to raise your voice for no member of the species of jinn or humankind would listen to your adhan without acting as a witness for you on the Day of Judgement.

Having said this, I would rush to add: If a person is praying alone in a Masjid where the Jama`ah has been performed, he should not raise the voice while doing so.

Almighty Allah knows best.