There are innumerable powerful demigods who look over the external management of the material world. They are all different assisting hands of Lord Vāsudeva. Even Lord Śiva and Lord Brahmā are included in the list of demigods, but Lord Viṣṇu, or Vāsudeva, is always transcendentally situated.
(Srimad Bhagavatam----1:2:28-29----purport).

Viṣṇu, being transcendental to all the modes, is always aloof from materialistic affection. This has already been explained. From Brahmā there is Rudra (Śiva), who is in charge of the mode of ignorance or darkness. He destroys the whole creation by the will of the Lord. Therefore all three, namely Brahmā, Viṣṇu and Śiva, are incarnations of the Garbhodakaśāyī Viṣṇu.
(Srimad Bhagavatam----1:3:5----purport).

In different millennia there are different incarnations, and they are innumerable, although some of them are very prominent, such as Matsya, Kūrma, Varāha, Rāma, Nṛsiṁha, Vāmana and many others. These incarnations are called līlā incarnations. Then there are qualitative incarnations such as Brahmā, Viṣṇu, and Śiva (or Rudra) who take charge of the different modes of material nature.
(Srimad Bhagavatam----1:3:5----purport).

Lord Viṣṇu is nondifferent from the Personality of Godhead. Lord Śiva is in the marginal position between the Personality of Godhead and the living entities, or jīvas. Brahmā is always a jīva-tattva. The highest pious living being, or the greatest devotee of the Lord, is empowered with the potency of the Lord for creation, and he is called Brahmā.
(Srimad Bhagavatam----1:3:5----purport).

Lord Śiva is not an ordinary living being. He is the plenary portion of the Lord, but because Lord Śiva is in direct touch with material nature, he is not exactly in the same transcendental position as Lord Viṣṇu. The difference is like that between milk and curd. Curd is nothing but milk, and yet it cannot be used in place of milk.
(Srimad Bhagavatam----1:3:5----purport).

The standard of perfection for a human being is to develop the attributes up to seventy-eight percent in full. The living being can never possess attributes like Śiva, Viṣṇu or Lord Kṛṣṇa. A living being can become godly by developing the seventy-eight-percent transcendental attributes in fullness, but he can never become a God like Śiva, Viṣṇu or Kṛṣṇa.
(Srimad Bhagavatam----1:3:28----purport).

According to the reading matter, either kaḥ or arkaḥ, there are two references in the Purāṇas. Kaḥ means Brahmā, who once became allured by his daughter and began to follow her, which infuriated Śiva, who attacked Brahmā with his trident. Brahmājī fled in fear of his life. As far as arkaḥ is concerned, there is a reference in the Vāmana Purāṇa. There was a demon by the name Vidyunmālī who was gifted with a glowing golden airplane which traveled to the back of the sun, and night disappeared because of the glowing effulgence of this plane. Thus the sun-god became angry, and with his virulent rays he melted the plane. This enraged Lord Śiva. Lord Śiva then attacked the sun-god, who fled away and at last fell down at Kāśī (Vārāṇasī), and the place became famous as Lolārka.
(Srimad Bhagavatam----1:7:18----purport).

Lord Śiva is a celebrated demigod who awards gifts to beggars. His name is therefore Āśutoṣa, or one who is pleased very easily. He is also called the Bhūtanātha, or the lord of the common folk, who are mainly attached to him because of his munificent gifts, even without consideration of the aftereffects. Rāvaṇa was very attached to Lord Śiva, and by easily pleasing him, Rāvaṇa became so powerful that he wanted to challenge the authority of Lord Rāma. Of course, Rāvaṇa was never helped by Lord Śiva when he fought with Rāma, the Supreme Personality of Godhead and the Lord of Lord Śiva. To Vṛkāsura, Lord Śiva awarded a benediction which was not only awkward, but also disturbing. Vṛkāsura became empowered, by the grace of Lord Śiva, to vanish anyone's head simply by touching it. Although this was awarded by Lord Śiva, the cunning fellow wanted to make an experiment of the power by touching the head of Lord Śiva. Thus the lord had to take shelter of Viṣṇu to save himself from trouble, and the Lord Viṣṇu, by His illusory potency, asked Vṛkāsura to make an experiment with his own head. The fellow did it and was finished himself, and so the world was saved from all sorts of trouble by such a cunning beggar of the demigods. The excellent point is that Lord Śiva never denies anyone any sort of gift. He is therefore the most generous, although sometimes some kind of a mistake is made.
(Srimad Bhagavatam----1:12:23----purport).

Gāndhārī: The ideal chaste lady in the history of the world. She was the daughter of Mahārāja Subala, the King of Gāndhāra (now Kandahar in Kabul), and in her maiden state she worshiped Lord Śiva. Lord Śiva is generally worshiped by Hindu maidens to get a good husband. Gāndhārī satisfied Lord Śiva, and by his benediction to obtain one hundred sons, she was betrothed to Dhṛtarāṣṭra, despite his being blind forever.
(Srimad Bhagavatam----1:13:3-4----purport).

Durvāsā Muni: A powerful mystic brāhmaṇa determined to observe the principles of religion with great vows and under strict austerities. His name is associated with many historical events, and it appears that the great mystic could be both easily satisfied and easily annoyed, like Lord Śiva. When he was satisfied, he could do tremendous good to the servitor, but if he was dissatisfied he could bring about the greatest calamity. Kumārī Kuntī, at her father's house, used to minister all kinds of services to all great brāhmaṇas, and being satisfied with her good reception Durvāsā Muni blessed her with a power to call any demigod she desired. It is understood that he was a plenary incarnation of Lord Śiva, and thus he could be either easily satisfied or annoyed. He was a great devotee of Lord Śiva, and by Lord Śiva's order he accepted the priesthood of King Śvetaketu because of the King's performance of sacrifice for one hundred years.
(Srimad Bhagavatam----1:15:11----purport).

By the grace of the Supreme Personality of Godhead Śrī Kṛṣṇa, all the demigods, including Lord Śiva, were pleased with Arjuna. The idea is that one who is favored by Lord Śiva or any other demigod may not necessarily be favored by the Supreme Lord Śrī Kṛṣṇa. Rāvaṇa was certainly a great devotee of Lord Śiva, but he could not be saved from the wrath of the Supreme Personality of Godhead Lord Rāmacandra. And there are many instances like that in the histories of the Purāṇas. But here is an instance where we can see that LordŚiva became pleased even in the fight with Arjuna.
(Srimad Bhagavatam----1:15:12----purport).

N.B. Pranam dearest devotees. Hare Krishna. If you have a set of the Bhagavatam, you can read the prayers said by Lord Shiva. As part of my night-time Sadhana, I read the Lord Shiva prayers from S.B. 4:24:33 to 4:24:68 . I know it by heart also. You can read it daily and also memorize it by heart. With love and best wishes, take care, bye.