Lord Shiva is worshipped in Linga form
Once upon a time the Sanata kumara asked Nandikeshvara (नंदिकेश्वर) on the mountain Mandara, he asked
शिवान्यदेववश्यानां सर्वेषामपि सर्वतः
वेरमात्रं च पूजार्थं श्रुतं दृष्टं च भूरिशः ।
शिवमात्रस्य पूजायां लिङ्गं वेरं च दृष्यते – Shiv Mahapurana , Vidyesvara Samhita 5.18
We see and hear multiple idols for every god in this world except Lord Shiva. Why only Lord Shiva is worshiped in both Linga form and idol form ?
Nandikeshvara replied to this question
शिवस्य ब्रह्मरूपत्वान्निष्कलत्वाच्च निष्कलम्
लिङ्गं तस्यैव पूजायां सर्ववेदेषु सम्मतम् ।
तस्यैव सकलत्वाच्च तथा सकलनिष्कलम् ॥ – Shiv Mahapurana , Vidyesvara Samhita 5.20-21
Since Lord Shiva is brahman who is formless, therefore the Linga is seen as his form. Vedas also have uttered the same. He alone is the whole. He is the one with form and formless too.
Fight between Lord Brahma and Vishnu
As mentioned in Shiv Mahapurana , Vidyesvara Samhita chapter 5 verses 27-30
पुरा कल्पे महाकाले प्रपन्ने लोकविश्रुते ।
अयुध्येतां महात्मानौ ब्रह्मविष्णू परस्परम् ॥ 27
तयोर्मानं निराकर्तुं तन्मध्ये परमेश्वरः ।
निष्कलस्तम्भरूपेण स्वरूपं समदर्शयत् ॥ 28
ततः स्वलिङ्गचिह्नत्वात् स्तम्भतो निष्कलं शिवः ।
स्वलिङ्गं दर्शयामास जगतां हितकाम्यया ॥ 29
तदाप्रभृति लोकेषु निष्कलं लिङ्गमैश्वरम् ।
सकलं च तथा वेरं शिवस्यैव प्रकल्पितम् ॥ 30
Nandikeshvara further mention an event of past where Lord Brahma and Lord Vishnu indulges in a fight over who is supreme. Lord Shiva to end there arrogance came out in the form of pillar (स्तम्भ) between them. With a desire to bless this world, Lord Shiva came out of that pillar, therefore that Linga is seen as symbol of Lord Shiva.
Since that time Lord Shiva is worshipped as formless in Linga form and with form in idols.
