Who composed the Mahishasura Mardini stotram?
Was it Adi Sankaracharya ?
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As commented, some says it is attributed to both Ramakrishna Kavi and Adi Shankaracharya. I'm here talking about what I've found:
Mahishasuramardini Stotra is a part of Bhagavatipadyapushpanjalistotra (भगवतीपद्यपुष्पांजलिस्तोत्र) which is written by Ramakrishna Kavi.You can read the full Bhagavati Padya Pushpanjali Stotra here in Sanskrit or transliteration.
It can be seen that After 6th verse of Bhagavati Padya Pushpanjali Stotra, Mahishasur Mardini Stotra starts which have 27 verses and then remains another three verses of Bhagavati Padya Pushpanjali Stotra. Verse 29 mention the author of Stotra who is Ramakrishna Kavi
रमयति किल कर्षस्तेषु चित्तं नराणामवरजवरयस्माद्रामकृष्णः कवीनाम् ।
अकृत सुकृतिगम्यं रम्यपद्यैकहर्म्यं स्तवनमवनहेतुं प्रीतये विश्वमातुः ॥ २९॥
ramayati kila karShasteShu chittaM narANAmavarajavarayasmAdrAmakR^iShNaH kavInAm |
akR^ita sukR^itigamyaM ramyapadyaikaharmyaM stavanamavanahetuM prItaye vishvamAtuH || 29||
Sanskrit documents page on Mahishasura Mardini Stotra also mentions that at the end:
The stotra is part of bhagavatIpadyapuShpA.njalIstotra written by Shri Ramakrishna Kavi.