It is a confirmed Sunnah for men to make the Adhan and Iqamah for prayer whether one is praying alone or in a congregation, but women are not required to make the Adhan or Iqamah. However, if a man performs prayer individually without making the Adhan or the Iqamah, his prayer is valid and he is not required to repeat it. It is preferable to make the Adhan and the Iqamah when praying alone.
Dr. Husam al-Din Ibn Musa `Afana, professor of Principles of Islamic Jurisprudence at Al-Quds University, Palestine, stated that: “The Iqamah, like the Adhan, is a confirmed Sunnah for males whether one prays alone or in a congregation, but women are not required to make the Adhan or Iqamah. `Uqbah ibn `Amir said that he heard the Prophet (peace and blessings be upon him) say, “Your Lord, the Exalted, is amazed (and pleased) by one who is watching sheep in his pasture, then goes to the mountain to make the call to prayer and pray. Allah, the Exalted, says, ‘Look at my slave there who makes the call to prayer and establishes the prayer out of fear of Me. I have forgiven my slave and have allowed him to enter Paradise.’” (Reported by Ahmad, Abu Dawud and an-Nasa’i)
As for the one who prays alone without making the Adhan or Iqamah, his prayer is valid and he is in no need to repeat it. Imam an-Nawawi explains the opinions of scholars regarding the Adhan and Iqamah stating that the Shafi`i opinion is that they are Sunnah for all prayers whether one is resident or on a journey, praying alone or in congregation, and that they are not obligatory at any time. So, if one does not make them, then the prayer is valid whether it is individual or congregational prayer. An-Nawawi also said that this is the opinion of Abu Hanifah and his followers, and of Ishaq ibn Rahwayh, and As-Sarakhsi reports that it is the opinion of the majority of scholars. The Hanbali scholar al-Kharqi states that the prayer of a person who offers prayer without making the Adhan or Iqamah is valid and he is not required to repeat it, but it is detestable to do so (i.e., to pray without making the Adhan and Iqamah). Ibn Qudamah al-Maqdisi in his Mughni comments, “I do not know any scholar who disputes this opinion save `Ata’. However the majority opinion is the most correct.”
This is supported by the hadith reported by Muslim on the authority of Al-Aswad and `Alqama who said: We came to the house of `Abdullah ibn Mas`ud. He said, ‘Have these people said prayer behind you?’ We said, ‘No.’ He said, ‘Then stand up and say the prayer.” He neither ordered us to say Adhan nor Iqamah.’”