Those conditioned souls who identify with this illusory material nature and are proud of it, and who do not care to know about the Supreme Lord, are subjugated by the Lord's illusory potency, who is known variously as Mahā Kālī, Cāṇḍī, and Durgā, and who pierces them with her trident of the threefold miseries. These demoniac jīvas are forced into slavery by the illusory potency—Kālī, or Mahāmāyā. The Bhagavad-gītā, which is the essence of all the Vedic scriptures, was compiled for the deliverance of the conditioned souls. By studying the Gītā carefully, a jīva takes shelter of the Supreme Lord's lotus feet and attains liberation from the merry-go-round of repeated suffering in the material world.
(Renunciation Through Wisdom).

The Lord says that His external potency—Mahā-māyā, or Kālī-serves Him in the form of the internal, spiritual potency. The jīva must allow this spiritual potency to influence him freely, without interference from the false ego, which makes the him think he is the doer. Thus surrendering to the Lord is the method prescribed to reach the highest stages of devotional service.
(Renunciation Through Wisdom).

Kṛṣṇa took compassion upon Brahmā because of his inability to see how Kṛṣṇa was displaying the forms of Viṣṇu and transforming Himself into calves and cowherd boys, and thus, while fully manifesting the Viṣṇu expansions, He suddenly pulled His curtain of yogamāyā over the scene. In the Bhagavad-gītā it is said that the Supreme Personality of Godhead is not visible due to the curtain spread by yogamāyā. That which covers the reality is mahā-māyā, or the external energy, which does not allow a conditioned soul to understand the Supreme Personality of Godhead beyond the cosmic manifestation. But the energy which partially manifests the Supreme Personality of Godhead and partially does not allow one to see is called yogamāyā. Brahmā is not an ordinary conditioned soul. He is far, far superior to all the other demigods, and yet he could not comprehend the display of the Supreme Personality of Godhead; therefore Kṛṣṇa willingly stopped manifesting any further potency. The conditioned soul not only becomes bewildered but is completely unable to understand. The curtain of yogamāyā was drawn so that Brahmā would not become more and more perplexed.
(Krsna Book).

The words used in this connection in Śrīmad-Bhāgavatam are bhagavān api. This means that although Kṛṣṇa is the Supreme Personality of Godhead and thus has no desire that needs to be fulfilled (because He is always full with six opulences), He still wanted to enjoy the company of the gopīs in the rāsa dance. Bhagavān api signifies that this dance is not like the ordinary dancing of young boys and young girls. The specific words used in Śrīmad-Bhāgavatam are yogamāyām upāśritaḥ, which mean that this dancing with the gopīs is on the platform of yogamāyā, not mahāmāyā. The dancing of young boys and girls within the material world is in the kingdom of mahāmāyā, or the external energy.
(Krsna Book).

The rāsa dance of Kṛṣṇa with the gopīs is on the platform of yogamāyā. The difference between the platforms of yogamāyā and mahāmāyā is compared in the Caitanya-caritāmṛta to the difference between gold and iron. From the viewpoint of metallurgy, gold and iron are both metals, but the quality is completely different. Similarly, although the rāsa dance and Lord Kṛṣṇa's association with the gopīs appear like the ordinary mixing of young boys and girls, the quality is completely different. The difference is appreciated by great Vaiṣṇavas because they can understand the difference between love of Kṛṣṇa and lust.
(Krsna Book).

On the mahāmāyā platform, dances take place on the basis of sense gratification. But when Kṛṣṇa called the gopīs by sounding His flute, they very hurriedly rushed toward the spot of the rāsa dance with the transcendental desire to satisfy Kṛṣṇa. The author of Caitanya-caritāmṛta, Kṛṣṇadāsa Kavirāja Gosvāmī, has explained that lust means sense gratification, and love also means sense gratification—but for Kṛṣṇa. In other words, when activities are enacted on the platform of personal sense gratification, they are called material activities, but when they are enacted for the satisfaction of Kṛṣṇa, they are spiritual activities. On any platform of activities, the principle of sense gratification is there. But on the spiritual platform, sense gratification is for the Supreme Personality of Godhead, Kṛṣṇa, whereas on the material platform it is for the performer. For example, on the material platform, when a servant serves a master, he is trying to satisfy not the senses of his master but rather his own senses. The servant would not serve the master if the payment stopped. That means that the servant engages himself in the service of the master just to satisfy his own senses. On the spiritual platform, however, the servitor of the Supreme Personality of Godhead serves Kṛṣṇa without payment, and he continues his service in all conditions. That is the difference between Kṛṣṇa consciousness and material consciousness.
(Krsna Book).

Māyāvatī had mystic knowledge of supernatural powers. Supernatural powers are generally known as māyā, and to surpass all such powers there is another supernatural power, called mahā-māyā. Māyāvatī had the knowledge of the mystic power of mahā-māyā, and she delivered to Pradyumna this specific energetic power in order to defeat the mystic powers of the Śambara demon. Thus being empowered by his wife, Pradyumna immediately went before Śambara and challenged him to fight. Pradyumna addressed him in very strong language, so that his temper would be agitated and he would be moved to fight. At Pradyumna's words, the demon Śambara, being insulted, felt just as a snake feels after being struck by someone's foot. A serpent cannot tolerate being kicked by another animal or by a man, and it immediately bites its opponent.
(Krsna Book).

In the above-quoted verse from Bhagavad-gītā, the words daivīṁ prakṛtim refer to the control of the internal potency, or pleasure potency, of the Supreme Personality of Godhead. This pleasure potency is manifested as Śrīmatī Rādhārāṇī, or Her expansion Lakṣmī, the goddess of fortune. When the individual jīva souls are under the control of the internal energy, their only engagement is the satisfaction of Kṛṣṇa, or Viṣṇu. This is the position of a mahātmā. If one is not a mahātmā, he is a durātmā, or a cripple-minded person. Such mentally crippled durātmās are put under the control of the Lord's external potency, mahāmāyā.
Indeed, all living entities within this material world are under the control of mahāmāyā, whose business is to subject them to the influence of threefold miseries: adhidaivika-kleśa (sufferings caused by the demigods, such as droughts, earthquakes and storms), adhibhautika-kleśa (sufferings caused by other living entities like insects or enemies), and adhyātmika-kleśa (sufferings caused by one's own body and mind, such as mental and physical infirmities). Daiva-bhūtātma-hetavaḥ: the conditioned souls, subjected to these three miseries by the control of the external energy, suffer various difficulties.
(Nectar of Instruction).

The difference between executing ordinary religious activities and devotional service is very great. By executing religious rituals one can achieve economic development, sense gratification or liberation (merging into the existence of the Supreme), but the results of transcendental devotional service are completely different from such temporary benefits. Devotional service of the Lord is ever green, and it is increasingly transcendentally pleasing. Thus there is a gulf of difference between the results derived from devotional service and those derived from religious rituals. The great spiritual energy known as jaḍādhiṣṭhātrī, or mahāmāyā, the superintendent of the material world, and the material departmental directors, the demigods, as well as the products of the external energy of the Supreme Lord, are but perverted reflections of the opulence of the Supreme Lord. The demigods are actually order carriers of the Supreme Lord, and they help manage the material creation. In Brahma-saṁhitā it is stated that the workings of the supremely powerful superintendent, Durgā, are but shadowy indications of the workings of the Supreme Lord. The sun works just like the eye of the Supreme Lord, and Brahmā works just as the reflected light of the Supreme Lord. Thus all the demigods as well as the external energy herself, Durgādevī, and all the different departmental directors are but servants of the Supreme Lord in the material world.
(Teachings of Lord Caitanya).

In the spiritual world, there is another energy, the superior spiritual energy, or internal energy, which acts under the direction of yogamāyā. Yogamāyā is the internal potency of the Supreme Lord; she also works under the Lord's direction, but she works in the spiritual world. When the living entity puts himself under the direction of yogamāyā instead of mahāmāyā, he gradually becomes a devotee of Kṛṣṇa. Yet those who are after material opulence and material happiness place themselves under the care of the material energy, mahāmāyā, or under the care of material demigods like Lord Śiva and others.
(Teachings of Lord Caitanya).

In Śrīmad-Bhāgavatam it is found that when the gopīs of Vṛndāvana desired Kṛṣṇa as their husband, they prayed to the spiritual energy, yogamāyā, for the fulfillment of their desire. In the Sapta-śatī it is found that King Suratha and a merchant named Samādhi worshiped mahāmāyā for material opulence. Thus one should not mistakenly equalize yogamāyā and mahāmāyā.
(Teachings of Lord Caitanya).

In the Vāyu Purāṇa there is a description of Sadāśiva in one of the Vaikuṇṭha planets. That Sadāśiva is a direct expansion of Lord Kṛṣṇa's form for pastimes. It is said that Sadāśiva (Lord Śambhu) is an expansion from the Sadāśiva in the Vaikuṇṭha planets (Lord Viṣṇu) and that his consort, Mahāmāyā, is an expansion of Ramā-devī, or Lakṣmī.Mahāmāyā is the origin or birthplace of material nature.
(Sri Caitanya Caritamrta----1:6:79----purport).

Following the example of the gopīs, the devotees sometimes worship the goddess Kātyāyanī, but they understand that Kātyāyanī is an incarnation of Yogamāyā. The gopīs worshiped Kātyāyanī, Yogamāyā, to attain Kṛṣṇa as their husband. On the other hand, it is stated in the Sapta-śatī scripture that a kṣatriya king named Suratha and a rich vaiśya named Samādhi worshiped material nature in the form of goddess Durgā to attain material perfection. If one tries to mingle the worship of Yogamāyā with that of Mahāmāyā, considering them one and the same, he does not really show very high intelligence.
(Sri Caitanya Caritamrta----2:8:90----purport).

The idea that everything is one is a kind of foolishness indulged in by those with less brain substance. Fools and rascals say that the worship of Yogamāyā and the worship of Mahāmāyā are the same. This conclusion is simply the result of mental speculation, and it has no practical effect. In the material world, sometimes one gives an exalted title to an utterly worthless thing; in Bengal this is known as giving a blind child a name like Padmalocana, which means "lotus-eyed." One may foolishly call a blind child Padmalocana, but such an appellation does not bear any meaning.
(Sri Caitanya Caritamrta----2:8:90----purport).