Mahā-kailāsa-nilayā महा-कैलास-निलया (578)

Mahā-kailāsa is the abode of Śiva. This is far away from the existing Kailāsa mountains. In fact, mahā-kailāsa is beyond human comprehension. Śiva has various forms and mahā-kailāsa is the abode of Paramaśiva.  Since Lalitāmbikā is always present with Śiva, mahā-kailāsa is referred to as the abode of Lalithāi as well.  This interpretation is given in epics. 

The orifice (bindu) in sahasrāra is known as mahā-kailāsaSahasrāra is beyond the six-cakra-s (mūlādhāra to ājñā) in the human body.  Śiva is visualised here in the form of a bindu (dot). Since She conjoins Śiva here in Her subtlest form, it is also referred as Her abode.  In the previous nāma three prastāra-s were discussed and one among them was Kailāsa prastāra, which is beyond the reach of Vāc Devi-s, the authors of this Sahasranāma.  They have used prefix mahā to mean Her best qualities and there are thirty seven such nāma-s in this Sahasranāma.

Mṛuṇāla-mṛdu-dorlatā मृणाल-मृदु-दोर्लता (579)

Her arms are tender like lotus stalks.  Her subtlest form is kuṇḍalinī.  This form is compared to that of a lotus stem in nāma 111.

Mahānīyā महानीया (580)

She is adorable. Whatever praise one showers on Her, She becomes worthy of it. Possibly this could be the reason for using prefix mahā (great) in a number of nāma-s. 

Dayāmūrtī दयामूर्ती (581)

She is the embodiment of compassion, which is one of Her predominant qualities.  This is the reason for commencing this Sahasranāma with Śrī Mātā, the compassionate mother of the universe.  To emphasize Her compassion, this quality has been repeated in nāma-s 197, 326 and 992. Compassion becomes Her predominant quality because She also sustains those who do not think about Her even for a moment.  This means that they are losing out opportunities of liberation, offered by Her.

Mahā-sāmrājya-śālinī महा-साम्राज्य-शालिनी (582)

She magnificently controls all the planets forming part of this universe. Normally sāmrājya refers to cluster of kingdoms. For Her, kingdoms mean planets and earth forming only a tiny part of the universe controlled by Her.  Even the mahā-kailāsa is ruled by Her in Her capacity as the consort of Śiva.   

Ātma-vidyā आत्म-विद्या (583)

This nāma and the next two nāma-s talk about three types of vidyā-s (knowledge). 

Ātma vidyā means the knowledge about the Brahman, Brahma vidyā.  Brahman is also known as Ātman.  Nāma 727 is Śiva jñāna pradāyinī, which means that She imparts knowledge on Śiva who is known as the Brahman without attributes.  Since She imparts knowledge (vidyā) of the Supreme Ātman, she is addressed as Ātma-vidyā

Turya Gāyatrī is also said be Ātma-vidyāTurya Gāyatrī is

ka-e-la-hrīṁ-vākbaveśvarī-vidmahe ha-sa-ka-ha-la-hrīṁ-kāmeśvarī-ca-dhīmahī

 sa-ha-la-hrīṁ-tanna-śaktiḥ-pracodayāt ॥ 

क-ए-ल-ह्रीं-वाक्बवेश्वरी-विद्महे ह-स-क-ह-ल-ह्रीं-कामेश्वरी-च-धीमही । स-ह-ल-ह्रीं-तन्न-शक्तिः-प्रचोदयात् ॥

 There is a mantra called ātma-aṣṭākṣara mantra.  The mantra is

om-hrīṁ-hamsaḥ-sohaṁ-svāhā॥ ॐ -ह्रीं-हम्सः-सोहं-स्वाहा ॥

(this mantra is a part of Śrī vidyā cult).  She is said to be in the forms of turīya Gāyatrī and ātma-aṣṭākṣara vidyā (aṣṭākṣara means eight alphabets). 

Mahā-vidyā महा-विद्या (584)

Knowing Ātman within, is the process of Self-realization and such knowledge is known as mahā vidyā as per the previous nāma.  This nāma says that Ātma-vidyā is the best of all vidyā-s (knowledge).  Knowing the Ātman within makes a person not to distinguish between pleasures and pains.  Such a person always stays connected with Her and enjoys perpetual bliss, leading to no more births.  Pleasure and pain are felt only if one is born. 

There is another interpretation which says that Vanadurgā vidyā is mahā vidyā. There is a scripture by name Vanadurgā saptasatī consisting of seven hundred verses. Almost every verse consists of mūla mantra. This is extremely powerful and its recitation is sure to drive away all evil forces. Mūla mantra of Vanadurgā consists of thirty seven bīja-s and is as follows:

uttiṣṭa puruṣi kiṁ svāpiṣi bhayaṁ me samupasthitaṁ yadi śakyamaśakyaṁ vā tanme bhagavati śamaya svāhā ||

ॐ उत्तिष्ट पुरुषि किं स्वापिषि भयं मे समुपस्थितं यदि शक्यमशक्यं वा तन्मे भगवति शमय स्वाहा॥

Śrī-vidyā श्री-विद्या (585)

Śrī-vidyā is Pañcadaśī mantraViṣṇu purāṇa refers to four types of vidyā-s. They are yajñā-vidyā (deals with karma-s), mahā-vidyā (rituals), guhya-vidyā (secretive worship), ātma-vidyā (knowledge of Self). Pañcadaśī and ṣodaśī mantra-s are considered as most secretive. These mantra-s, if properly initiated and recited as per the prescribed rules, one is bound to attain liberation.