Its history is shrouded in mystery (like some other religious scriptures),
but here are a few things several people seem to agree on:
It is something which does not figure in Valmiki Ramayanam (though some
northern versions do include it supposedly), but almost every publication
of AH would say it appears in the 107th sarga of Yuddha Kaandam. There is *some*
version of Ramayanam that is supposed to have it.

It has some similarity to the Bhagavad Gita in the situation in which
it is rendered. It has taken up a controversial bent sometimes because Agastya
Maharishi is giving Rama the "mantram" to re-energize himself and go to war
with Ravana - Rama is not supposed to need any mantram to do whatever He
pleases : is the source of the controversy.

There are dozens of websites which give the verses (with varying differences in
spelling and meaning). The exploration here is to get at the meanings of each
of the Sanskrit words, investigate roots and other related words.

[1] "AdityaHrdayam", Translated by Swami Tejomayananda, Central Chinmaya Mission Trust
[2] "AdityaHrdayam", Translated by S. Venkatasubramanyam, Sri Ramakrishna Math
[3] "The Practical Sanskrit-English Dictionary", Vaman Shivram Apte, Motilal Banarsidass Publishers
[4] "A Sanskrit English Dictionary", M. Monier-Williams, Motilal Banarsidass Publishers
Many thanks to Balaji and Mani for proof-reading.

tatO yuddha parishrAntam samarE cintayAsthitam [1.txt]
rAvaNam cAgratO dR^iShTvA yuddhAya samupasthitam

daivatai: ca samAgamya draShTum abhyAgatOraNam [2.txt]
upAgamya: abravIt rAmam agastyO bhagavAn R^ishi:

rAma rAma mahA bAhO shrunu guhyam sanAtanam [3.txt]
yEna sarvAn arIn vatsa samarE vijayiShyasi

AdityahR^idayam puNyam sarvashatruvinAshanam [4.txt]
jayAvaham japennityam akshayyam paramam shivam

sarva ma~ngala mAngalyam sarva pApa praNAshanam [5.txt]
cintA shOka prashamanam Ayu: vardhanam uttamam

rashmimantam samudyantam devAsura namaskRtam [6.txt]
pUjayasva vivasvantam bhAskaram bhuvaneshvaram

sarvadevAtmakO hyESha tEjasvI rashmibhAvana: [7.txt]
ESha devAsuragaNAn lokAn pAti gabhastibhi:

ESha: brahmA ca vishnushca shiva: skanda: prajApati: [8.txt]
mahEndrO dhanada: kAlO yama: sOmO hyapAm pati:

pitarO vasava: sAdhyA hi ashvinOu marutO manu: [9.txt]
vAyu: vahni: prajAprANa R^itukartA prabhAkara:

Aditya: savitA sUrya: khaga: pUShA gabhastimAn [10.txt]
suvarNasadrushO bhAnurvishvarEtA divAkara:

haridashva: sahasrArci: saptasaptirmarIcimAn [11.txt]
timirOnmathana: shambhustvaShTA mArtaNda anshumAn

hiraNyagarbha: shishirastapanO bhAskarO ravi: [12.txt]
agnigarbhO aditE: putra: sha.Nkha shishiranAshana:

vyOmanAtha: tama: bhEdI ruk yaju: sAmapAraga: [13.txt]
ghanavruShTirapAm mitrO vindhya vIthI plavangama:

AtapI maNDalI mrutyu: pi.Ngala: sarvatApana: [14.txt]
kavirvishvO mahAtEjA raktassarvabhavOdbhava:

nakshatra grahatArANAm adhipO vishvabhAvana: [15.txt]
tejasAm api tejasvI dvAdashAtmannamOstutE

nama: pUrvAya girayE pashcimAyAdrayEnnama: [16.txt]
jyOtirgaNAnAm patayE dinAdipatayE nama:

jayAya jayabhadrAya haryashvAya namO nama: [17.txt]
namO nama: sahasrAmsha AdityAya namO nama:

nama ugrAya vIrAya sAra.NgAya namOnnama: [18.txt]
nama: padmaprabOdhAya mArtaNDAya namOnnama:

brahmEshAnAcyutEshAya sUryAyAditya varcasE [19.txt]
bhAsvatE sarva bhakshAya rOudrAya vapuShE nama:

tamOghnAya himaghnAya shatrughnAyAmitAtmanE [20.txt]
kRtaghnahanAya dEvAya jyOtiShAm patayEnnama:
(kRtaghnaghnAya...)

taptacAmIkarAbhAya harayE vishva karmaNE [21.txt]
namastamO$bhinighnAya rucayE lOkasAkshiNE

nAshayatyESha vaibhUtam tadEva sR^ijati prabhu: [22.txt]
pAyatyESha tapatyESha varShatyESha gabhastibhi:

ESha suptEShu jAgarti bhUtEShu pariniShThita: [23.txt]
ESha EvAgnihOtram ca phalam caivAgnihOtriNAm

vEdAshca kratavashcaiva kratUnAm phalamEva ca [24.txt]
yAni kR^ityAni lOkEShu sarva ESha ravi: prabhu:

EnamApatsu kR^icchEShu kAntArEShu bhayEShu ca [25.txt]
kIrtayan puruSha: kashcinnAvasIdati rAghava

pUjayasvainamEkAgrO devadevam jagatpatim [26.txt]
Etat triguNitam japtvA yuddhEShu vijayiShyasi

asminkshaNE mahAbAhO rAvaNam tvam vadhiShyasi [27.txt]
EvamuktvA tadAgastyO jagAma ca yathAgatam

EtacchrutvA mahAtEjA naShTashOkO$bhavattadA [28.txt]
dhArayAmAsa suprItO rAghava: prayatAtmavAn

Adityam prEkshya japtvA tu param harShamavAptavAn [29.txt]
trirAcamya shucirbhUtvA dhanurAdAya vIryavAn

rAvaNam prEkshya hR^iShTAtmA yuddhAya samupAgamat [30.txt]
sarvayatnEna mahatA vadhE tasya dhR^itO$bhavat

atha raviravadan nirIkshya rAmam [31.txt]
muditamanA: paramam prahR^iShyamANa:
nishicarapatisankshayam viditvA
suragaNamadhyagatO vacastvarEti