I've seen in many places, "Srimathe Varavara Munayeh Nama:" along with "Srimate Ramanujayah Nama:"
Can someone tell the meaning of "Srimathe Varavara Munaye Nama:" and the acharya/Guru the salutations refer to?
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Srimad Varavara Munayeh Nama - Salutations to Varava Muni
Varavara muni is the other name of Manavala Mamunigal
Manavala Mamunigal was born in 1370 at Alwarthirunagiri in Tamil Nadu. His parents were Tigalakidanthan Tirunaveerudaiya Piran Tadar Annar and Sriranga Nachiyar.His father was the son-in-law and also a disciple of Kollikavala Dasar, a junior disciple of Pillai Lokacharya. His parents named him Alagiya Manavalan (beautiful groom) after the deity Ranganathaswamy of Srirangam.
Manavalan was schooled by father and maternal grandfather, who taught him the Vedas, Vedanta, and the Naalayira Divya Prabandam. He married at the age of 16, and moved from Sikkil Kidaram to Alwarthirunagari to become the disciple of the acharya Tiruvaymolipillai.
Tiruvaymolipillai was not instrumental in reviving the archa tirumeni (idol) of Ramanuja at Alwarthirunagari and in building a temple for him. He put the young Manavalan in charge of the temple and gave him to title of Yatheendra Pravana in recognition of his devotion to Ramanuja. It was around this time that Manavalan wrote Yathiraja Vimsati, which is considered to be the very essence of the exalted Ramanuja Nootrantati.
Journey towards Srirangam
On his deathbed, Tiruvaymolipillai instructed Manavalan to learn and propagate the Sri Bhasya, and to spend most of his time in propagating and preaching the arulicheyal (Divya Prabhandam) of the Alvars. He also asked Manavalan to stay at Srirangam and perform service to Ranganatha, as his predecessors had done.
Manavalan was inconsolable upon the death of his master. He immersed himself completely into studying and delivering discourses on Divya Prabandham, and rahasyas. Word of his abilities spread and he gained various disciples. Prominent among them was Sri Alagiya Varadar, who undertook sanyasashrama (asceticism) from Manavalan. The sanyasa name was given as "Ramanuja Jeeyar" (also known as Ponnadikkal Jeeyar). Thus began the most illustrious jeeyar matha in the Sri Vaishnava sampradaya, the Vanamamalai matha, that continues the great unbroken lineage of acharyas to this day.
Intending to fulfil the wishes of his acharya, Manavalan and his disciples left for Srirangam, spending some time at Srivilliputhur, the birthplace of Andal, on their journey.
Life at Srirangam and visit to Kanchipuram
Srirangam, at that point, was facing the worst consequences of the Muslim invasion that took place in the early 14th century. It was structurally dilapidated, sacramentally bare, intellectually barren and spiritually, socially and morally corrupt. Misuse of rights, corruption and disorder were rampant. Manavalan had to exert tremendous effort and bring to force his organizational skills to restore the original pristine glory for daily sacramental and festival procedures at Srirangam, without antagonizing the people who were functioning in different capacities at that point in time. He realized the importance of bringing the focus back to the essential tenets of Sri Vaishnavism and achieved this objective by bringing to fore scholarly works of acharyas, that had hitherto been pushed into the background. As a result of his devotion, Manavalan was put in charge of everyday temple administration, as well as anointed the leader for all the Sri Vaishnavas of his time.
With normalcy returning to Srirangam, Manavalan set on a pilgrimage to Kanchipuram, Tirumala, and Sriperumbudur, after seeking the blessings of Ranganatha. Manavalan paid his obeisance to Srinivasa at Tirumala, and reached Kanchipuram. At the request of his disciples to glorify the form of Vishnu at Kanchipuram, he composed the Devaraja Mangalam, which praises the glory of Varadharaja in thirteen verses. At Sriperumbudur, Manavalan worshipped Ramanuja, and sought his blessings to formally study Sri Bhasya under an acharya. Ramanuja directed him to Kidambi Manavalan, a descendant of Kidambi Achan. Manavalan exhibited his erudition and scholarship by grasping the intricacies of Sri Bhasya deftly, and then simultaneously expounding it to other disciples. The discourse took place at Yathothkari temple at Tiruvekkaa, where his idol is seen showing the vyakhyana mudra (the teaching gesture) to commemorate this event.
After visiting several other holy places, Manavalan returned to Srirangam to fully manage the temple affairs. He undertook sanyasashrama (asceticism) from Sri Sadagopa Jeeyar of Alwarthirunagari (who was his classmate earlier) at Srirangam, to fully involve himself in service to Sri Vaishnavism. It was during this time that he received the appellation Alagiya Manavala Mamuni.
At this point of time, some prominent scholars, namely, Koil Kanthatai Annan, Prathivadhi Bhayankaram Annan, Erumbi Appa, and Appillai became his disciples.
Manavala Mamunigal continued to live in Srirangam, and involved himself completely in writing commentaries for works of Pillai Lokacharya. He wrote elaborate commentaries for three of Pillai Lokacharya's rahasya granthas (secret texts), namely Mumukshupadi, Sri Vachana Bhushanam, and Thathvathrayam. He also wrote commentaries on the works of swami Arulala Perumal Emperumanar - Gnana Saram and Prameya Saram. He penned commentaries on some decads of Periyalvar Tirumoli, for which the original commentaries of Periyavaccan Pillai were supposed to be lost. In addition, he provided the gist of Nammalvar's Tiruvaymoli in the form of poetic verses tuned in the antati metre in his magnum opus, Tiruvaymoli Nootrantati. Manavalan extolled the greatness of the Alvars and the acharyas who wrote commentaries on Tiruvaymoli in his Upadesa Ratnamalai, or the gem-studded garland of instructions. His swansong, Arti Prabandham - a work composed out of utter despair at having to live in this material world - bears resemblance in part to his earlier Sanskrit work titled Yatiraja Vimsati.
After some time, he returned to Alwartirunagari and started to write commentaries for Acharya Hrudayam. This is a seminal work written by Alagiya Manavalaperumal Manavalan (Pillai Lokacharya's brother), which lays bare the philosophy and basic tenets of Sri Vaishnavism, with words chosen from Nammalvar's Tiruvaymoli. The text was written completely in Manipravalam, but when trying to teach Acharya Hrudayam, Mamunigal encountered some difficulties. So, he decided to consult with Ayee Jananyacharya, who was a co-disciple of Tiruyaymolipillai. Ayee was on his way to Alwartirunagari to meet Manavalan. They both met at the outskirts of Alwartirunagari and returned to Manavalan's residence, and the latter studied the secrets of the Acharya Hrudayam.
Source: https://en.wikipedia.org/wiki/Manavala_Mamunigal ( You can find more about him here )