Ashvamedha Yajna (अश्वमेधयज्ञः)
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One of the most confusing aspects of yajna to the modernist is horse sacrifice,(ashvamedha yajna) cow sacrifice( go medha yajna) and human sacrifice( purusha medha yajna). When seen from superficial point of view[a fact or an opinion?] and the western indologist point of view, it sounds that the followers of sanatana dharma brutally killed animals in the name of yajna. But understanding these yajna's for the Rishis gives complete understanding [clarification needed] and freed from confusion.
In Taittiriya Brahmana's ashvamedha prashna, ashvamedha is the Yajna that helps Rashtramshwamedhah, (nation-building). This kind of Yajna calls for great atma-samarpana. The horse of the yajna symbolises every aspect of the King, his prosperity, his power. It is this aspect of Rajatva (kinghood) that helps the Rashtra to prosper. Thus, it is this dedication of the King and the citizens that make RashtraVardhana (nation-building) possible.
The "Ashwo vai prajapatih" (Horse Yajna) is done with the motive of bringing all people together.
"सन्घ्रन्येस्ह्वयजते ! इमगम् जनतगम् सन्ग्रह्ननिति ||"
"sanghranyeshvayajate ! imagam janatagam sangrahnaniti ||
The Yajnas rooted in the Vedas have profound meaning at all levels (collective, social, personal) and in all aspects ranging from naimittika Karma to Nitya Karma till Mukti[a fact or an opinion?]. The Yajurveda terms the fight we undertake for our protection as Dharmic war.Kurukshetra becomes the field of yajna and devatas made Vishnu into the Yajna. From that Vishnu’s left hand, the bow appears and from the right, arrows. The Taittiriya aranyaka says this
This is the kshatra Yajna (Kshatriya sacrifice). The bow itself became AUM, the atma became shara (arrow), Brahman was the destination and when the arrow (atma) becomes one in consciousness of devotion then Moksha (liberation) is experienced. This is elaborated in the Mundaka Shruti.
It is undeniable fact that no civilization has flourished without the power of warrior class, of course when warrior class become only brutal then they are less than terrorist.[a fact or an opinion?]. Warrior is not one who knows how to take someone else's life alone, that is last resort he applied for protection of his country or culture[a fact or an opinion?]. But kshatriya means who is meant to protect.
Kshata means pain or danger and tra and one who frees. Therefore kshatriya means one who frees others from difficulty. Sri Rama told mother Sita in Ramayana about how is bow stands up hearing the plea of afflicted[clarification needed]. Therefore, ashvamedha yajna denotes and symbolizes the dedication of kshatriya or a dharmik king or a soldier for a dharmik cause[a fact or an opinion?]. Horse and kshatriya are synonymous, they symbolize power and prepared for protection. Protection does not happen without soldiers sacrificing their life and protection does not happen without using weapon judiciously[a fact or an opinion?]. All the devatas in the Dharmik tradition told weapons whether be it Shiva or Vishnu, even Devis are not exceptions to this rule[a fact or an opinion?]. Abrahamic faith may claim that Jesus did not use weapons, he forgave all but it is not secret that christianity spread with sword and strength[clarification needed][a fact or an opinion?].
We will find lot of explanation in Mahabharata and Ramayana about different ashvamedha yajnas.
The yajna being smaller than the smallest and greater than greatest is all-pervading and incomparable[a fact or an opinion?]. Even the relationship between man and woman has been described as Yajna. In the modern world, the relationship between men and women has been reduced to physical attraction[a fact or an opinion?]. Therefore to see the relationship between man and woman as the Yajna principle, it is important to have a Vedic Darshan (perspective)[a fact or an opinion?]. From the perspective of Sruti, everything is pure and is Yajna[a fact or an opinion?]. One who opposes the principle of Yajna is adharmic as they oppose the process of creation, maintenance and destruction as described in the Vedas[a fact or an opinion?]. Gita enunciates the Sattvic person’s vision from the Vedic perspective.
"ब्रह्मर्पनम् ब्रह्म हविह् |
ब्रह्मग्नौ ब्रह्मन हुतम् ब्रह्मैव तेन् गन्तव्य ब्रह्म कर्म समधिन || (Gita 4-24)"
"brahmarpanam brahma havih |"
"brahmagnau brahmana hutam brahmaiva ten gantavya brahma karma samadhina || (Gita 4-24)"
Brahman is offering, brahman is oblation, brahman is the havissu (the sanctified Prasadam). Brahman is Agni, the performer is the Purusha and the results reach the Brahman, this process is termed brahma karma samadhi of Karmayoga. This is how the yajna becomes the foundation for Vedanta Darshan.
No scope of errors
Alternate meaning; Ashva means kala or time and medha means purified. The performer of ashvamedha yajna get purified of all sins committed in any past life. The ashvamedha yajna was a double-edged sword, in that it could deliver great results and ensure an elevated life for the performer, but it could also prove disastrous if there were to be single lapse.  It was believed that brahma rakshasas attacked and destroyed the performer as soon as that single error was committed.  Brahma raksasas were brahmanas in their previous birth reborn as demon for sins they had committed in their past lives.  Whenever such yajnas took place, brahma raksasas would start hovering over the yajnika arena waiting for a single mistake. 
List of performers
There appeared many great kings who performed Ashvamedha Yajna. A few of the them are listed below:
|Maharaja Dasaratha||Dynasty of King Raghu (Raghuvamsa)||ऋष्यश्रृङ्गं पुरस्कृत्य कर्म चक्रृर्द्विजर्षभाः
अश्वमेधे महायज्ञे राज्ञोऽस्य सुमहात्मनः 
|Lord Ramachandra||Dynasty of King Raghu (Raghuvamsa)||अश्वमेधशतैरिष्ट्वा तथा बहुसुवर्णकैः
गवां कोट्ययुतं दत्त्वा विद्वद्भ्यो विधिपूर्वकम् असंख्येयं धनं दत्त्वा ब्राह्मणेभ्यो महायशाः
|Maharaja Prthu||Dynasty of Kashyapa||चरमेणाश्वमेधेन यजमाने यजुष्पतिम्
वैन्ये यज्ञपशुं स्पर्धन्नपोवाह तिरोहितः 
|King Purandra (Indra)||Dynasty of Kashyapa||हृत्या बलिसमः कृष्णे प्रह्राद इव सद्ग्रहः
आहर्तैषोऽश्वमेधानां वृद्धानां पर्युपासकः 
|Somadatta, Son of Krshashva||Dynasty of Dista(son of Vaivasvata Manu)||कृशाश्वात्सोमदत्तोऽभूद्योऽश्वमेधैरिडस्पतिम्
इष्ट्वा पुरुषमापाग्र्यां गतिं योगेश्वराश्रिताम् 
|Maharaja Ambarish||Dynasty of Nabhaga (son of Vaivasvata Manu)||ईजेऽश्वमेधैरधियज्ञमीश्वरं महाविभूत्योपचिताङ्गदक्षिणैः
ततैर्वसिष्ठासितगौतमादिभिर्धन्वन्यभिस्रोतमसौ सरस्वतीम् 
|Maharaja Sagar||Dynasty of Ikshvaku (son of Vaivasvata Manu)||सोऽश्वमेधैरयजत सर्ववेदसुरात्मकम् और्वोपदिष्टयोगेन
हरिमात्मानमीश्वरम् तस्योत्सृष्टं पशुं यज्ञे जहाराश्वं पुरन्दरः 
|Ushanaa, Son of Dharma||Dynsaty of Yadu||तेषां तु षट्प्रधानानां पृथुश्रवस आत्मजः
धर्मो नामोशना तस्य हयमेधशतस्य याट् 
|Maharaja Yudhisthir||Kuru dynasty||याजयित्वाश्वमेधैस्तं त्रिभिरुत्तमकल्पकैः
तद्यशः पावनं दिक्षु शतमन्योरिवातनोत् 
|Maharaja Parikshit||Kuru dynasty||हृत्या बलिसमः कृष्णे प्रह्राद इव सद्ग्रहः
आहर्तैषोऽश्वमेधानां वृद्धानां पर्युपासकः 
|Janamejaya (son of Pariksit)||Kuru dynasty||कालषेयं पुरोधाय तुरं तुरगमेधषाट्
समन्तात्पृथिवीं सर्वां जित्वा यक्ष्यति चाध्वरैः 
- Valmiki Ramayana (valmikiramayan.net) Baala Kanda, Sarga 12, verse 15-19
- Krishna Dvaipayana Vyasa (Bhagavata-Gita-Mahatmyam) Padma Purana (The Glories of the Bhagavad-gītā) Chapter 8
- Shubha Vilas (Ramayana, The Game of Life) Book 1 : Roar with courage page 34-36
- Valmiki Ramayana  Baala Kand, sarga 14 verse 2
- Valmiki Ramayana  Baala Kand, sarga 1 verse 94-95
- Bhaktivedanta Vedabase Bhagavata Purana 4.19.11
- Bhaktivedanta Vedabase Bhagavata Purana 1.12.25
- Bhaktivedanta Vedabase Bhagavata Purana 9.2.35-36
- Bhaktivedanta Vedabase Bhagavata Purana 9.4.22
- Bhaktivedanta Vedabase Bhagavata Purana 9.8.7
- Bhaktivedanta Vedabase Bhagavata Purana 9.23.33
- Bhaktivedanta Vedabase Bhagavata Purana 1.8.6
- Bhaktivedanta Vedabase Bhagavata Purana 9.22.37