Aigiri Nandini.

I like Aigiri Nandini and I got to know of it only recently. This song in praise of Goddess Durga is much more popular in the southern states than here in the North. It puts Durga in an amazing light. She is this absolutely beautiful woman, sweet and charming, and at the same time, she is the mother of the universe, the feeder of the triloka or the Three Worlds, one who takes care of all that could go wrong. She kicks sad demon asses for breakfast and raises war cries worthy of only the daughter of the Mountains and the Oceans. Durga is someone everyone can look up to. Men and women alike. 

I am not an authority on Sanskrit, at all. I read a lot of translations, some missing in a few details, and some misinterpreted, and referring to literal meanings of many of these words, came up with the following three paragraphs (the original poem has around 21 paragraphs!). 

अयि गिरिनन्दिनि नन्दितमेदिनि विश्वविनोदिनि नन्दिनुते
गिरिवरविन्ध्यशिरोऽधिनिवासिनि विष्णुविलासिनि जिष्णुनुते ।
भगवति हे शितिकण्ठकुटुम्बिनि भूरिकुटुम्बिनि भूरिकृते
जय जय हे महिषासुरमर्दिनि रम्यकपर्दिनि शैलसुते ॥ १ ॥

Praise be to you, daughter of the Mountains, praised by the world, who fills the world with joy and happiness, whom Nandi himself praises,

Who resides on the peak of the king of the mountains, Vindhya, who lives with Vishnu (as his sister) and is praised by Lord Indra,

O Goddess, wife of the lord with blue neck, the mother of the Universe, the creator of prosperity. 

Glory to you, O vanquisher of Mahishasura, O beautiful daughter of the Mountains.

सुरवरवर्षिणि दुर्धरधर्षिणि दुर्मुखमर्षिणि हर्षरते
त्रिभुवनपोषिणि शङ्करतोषिणि किल्बिषमोषिणि घोषरते
दनुजनिरोषिणि दितिसुतरोषिणि दुर्मदशोषिणि सिन्धुसुते
जय जय हे महिषासुरमर्दिनि रम्यकपर्दिनि शैलसुते ॥ २ ॥

You who shower even the Gods with your blessings, the one who defeated Duradhara and Durmukha, the joyous one, 

The nourisher of the three worlds, the consort of Shankara, the destroyer of sin and the one with the furious war cries,

The killer of Danu's and Diti's demon children, destroyer of the demons' pride, daughter of the Ocean.

Glory to you, O vanquisher of Mahishasura, O beautiful daughter of the Mountains.

अयि जगदम्ब मदम्ब कदम्ब वनप्रियवासिनि हासरते

शिखरि शिरोमणि तुङ्गहिमलय शृङ्गनिजालय मध्यगते ।
मधुमधुरे मधुकैटभगञ्जिनि कैटभभञ्जिनि रासरते
जय जय हे महिषासुरमर्दिनि रम्यकपर्दिनि शैलसुते ॥ ३ ॥

Glory to the mother of the Universe, my own mother, the dweller of the forests of Kadamba trees, who delights in laughter, 

Who resides on the jeweled peaks of the Himalayas, who walks mildly, and makes herself beautiful*

As sweet as honey, who humbled the demons Madhu and Kaitabha, and killed them, indulging in battle cries,

Glory to you, O vanquisher of Mahishasura, O beautiful daughter of the Mountains. 

*I have been told that in Indian scriptures Madhyagati (medium pace) is a mark of an ideal woman, and is part of her shringaar.