I think, I am closer to Kashmir Shaivism. Shiva does not create it. But we in our own ignorance take an illusion to be the truth. I have not studied it deeply because I got my answers from science. The link that Ameyatma gave is for South India Shaivism, the Nandinath Sect, which Vinayaka follows.
As far as I understand, the exact same 5 powers of Shiva are explained by Kashmiri Shaiva siddhAnta by Abhinav Gupta / Swami Lakshman joo
Shiva hides where the event triggered by the 'spanda' (first vibration) gives rise to the ripple effect of stone thrown in a still lake. All Shaiva will explain that mAyA is limitation owing to measurement, whereas Shiva in unbound, but they do mention that the world that arises is an effect from shiva but is Shiva after all.
Why this world is not an illusion (maya) in Kashmir Shaivism
Why this world is not an illusion (maya) in Kashmir Shaivism
आश्यानं चिद्रसस्यौघं साकारत्वमुपागतम् ।
जगद्रूपतया वन्दे प्रत्यक्षं भैरवं वपुः ।।८।।
aśyānaṁ cidrasasyaughaṁ sākāratvamupāgataṁ
jagadrūpata yā vande pratyakṣaṁ bhairavam vapuḥ // 9 (8)
Cidrasasyaughaṁ aśyānaṁ; cidrasa the coagulation of cit rasa is the universe, it is the universe, it is not anything else [other] than God consciousness. It is just God consciousness but [it’s] coagulated consciousness. Coagulated means that it is just like, it becomes hard to experience.
SWAMIJI: It is not illusion.
Jagadrūpata yā vande, I bow to this universe, which is pratyakṣaṁ bhairavam vapuḥ, this Bhairava has come with formation. [This] Bhairava can be photographed and that Bhairava cannot be photographed which is . . .
JOHN: Transcendental.
DENISE: Transcendental.
SWAMIJI: That is transcendental.
So this is also Bhairava. You must not be afraid of this God consciousness, which is coagulated in the formation of saṁsāra. So you should not get afraid from saṁsāra. There is no question, there is no room, for fearing this universe. Because the universe, as long as it is concerned, it is the actual formation of God consciousness in a coagulated form. That is the only difference.
There is another sect known as Nath Sect, centered in Gorakhpur, which the former Kings of Nepal followed. The head of the Sect, Yogi Adityanath, is presently the Chief Minister of Indias largest state, Uttar Pradesh.
Yes, I am glad you brough up the Nath sampraday/
For those who are not familiar with this sampradaya,
The NavaNath , nAth sampradAya is a very austere tradition of dhyAna, jnAna and bhakti.
It was a planned project of Shri Gurudev DattAtreya (VishNu avatAr of treta yuga) and Shiva.. Datta and Shiva's project plan to uplift mankind and make it kinder, bore fruit when their prayer to the 9 NArAyan forms was heard to manifest as the 9 nAtha (Lords, Gurus, authorities, caretakers)
The nAtha except for Meena nAtha are said to be svayambhu - and they lived a very austere forest life of yoga dhyana sanyAsa sAdhanA.
With their tapas and yoga siddhi they touched a large population in all areas they wandered, through towns and villages of thiose times.
The nAths, who were amshas and combinations of NArAyan(VishNu) and Shiva, were VishNu-Shiva bhakta , jnAni and yogis.
The first nAth of the Datta(VishNu) - Shiva team project was MachhindranAtha. DattAtreya took him to Badrinath at a young age, gave Guru diksha and raised him as a austere yogi.
His disciple GorakshanAtha knew the world through his beloved teacher Machhindranath (A NArAyaN form), who was the world to him, father, mother, friend, Guru and all.
GorakshanAth was said to be a 'pratipUra' of Shiva/ Mahadev / Shankar / Bholenath
Gahininath , a form of antariksha nArAyaNa appeared (manifested) as a baby/child when 12 year old Goraksha's sanjeevani vidya gained perfection.
Machhindra left Gahini with a couple in the nearby village and took Goraksha to Girnar, to DattAtreya per orders of Guru DattAtreya.
He left him there and went on a mission assigned to him. Goraksha cried, but eventually was trained first at Girnar by DattAtreya Himself (where Datta, the 3 sandhyA Gayatris being Himself, took the Gayatri forms and gave darshan to the 12 year old Goraksha ) , and later sent to Kailash under the strict observation of Shiva Mahadev Himself,
When Gorakshanath was a grown adult of 24 his sadhanA was complete, and he went searching for his Guru , Machhindranath.
Meanwhile, as planned and instructed by Machhindranath, when Gahini was old enough , Goraksha nath gave him Guru deeksha (became his guru as per plan)
Jalindar nath appeared out of a yadnya agni kunda and was a form of Agnidev. He went into involunrary samAdhi dhyAna in the forests. The king and queen could not retain this adopted child nor could other foster parents. He left for the woods.
Jalindar nath's disciple was KAneefnAth, also vibrant and brilliant.
The nAthas major assignments by their param Gurus Datta and Shiva, were to eradicate blind faith and bad or malpractices like black magic by some rare tantrics in remote pockets of the area. and also spread peace, community , brotherhood and love, help the poor and drive away hardships of whole communities.
Later, as predicted by Machhindranath and Gurudev Datta, Gahininath went on to establish a relatively easier path of bhakti and became the Guru of Nivruttinath, oldest brother of Sant DnyAneshwar (author of the first Marathi version and commentary, poetry on Bhagavad Geeta). It was said that by blessings of Gahininath the entire VArkari sampradAya of Vitthal bhakti came into being. The 2 dinDi , one from Tukaram's Dehu and DnyAneshwar's ALandi go to Pandharpur on Ashadhi and Kartiki ekadashi on foot each year till date. A tradition that goes back hundreds of years, centuries, of making the'wAri' (trip on foot) to Pandharpur.
The story of the 9 nAtha (nava nArAyan -- nava nAth) is found in "NavanAth Bhaktisaar"
Most of the places the 9 naths' feet touched were in Maharashtra, Gujrath (Girnar), Himalayas (Kailash, foothills), Badrinath...
Throughout their avatAr kArya, they were assisted time and again by Adi Shakti in the form of Parvati, Durga, Lakshmi, Gayatri, Saraswati.
There is a Marathi TV serial , currently on air, in India -- "Gatha NavanAthAnchi" It is quite informative, and just watching it makes you peaceful.
|| Om namo nArAyaNArya ||
|| Om namo Bhagavate VAsudevAya ||
|| Om namah: ShivAya ||
|| sarva mangala mAngalye shive sarvArtha sAdhike sharaNye trayambike devi nArAyaNi namostute ||