This grouping covers mantras from the Tantras and the Agamas. Many widely recited deity mantras are neither Vedic nor Tantric but Pauranic or stotra literature — those are listed separately below.
13 mantras
The single most quoted line of the Bhairava tantras: shaivi mukham ihochyate, here Shakti is called the face.
Bhairava's own answer to what he actually is: released from the reckoning of space and time, and unspeakable in the strict sense.
Two anushtubhs from the first patala of the Mundamala Tantra that name all ten Mahavidyas in order — the standard enumeration of the set.
Hanuman's root mantra — the bija हं with his name in the dative. The commonest Hanuman japa in daily practice.
One anushtubh that names all eight principal Bhairavas in order: Asitanga, Ruru, Chanda, Krodha, Unmatta, Kapali, Bhishana and Samhara.
The verse that opens the Ashta Bhairava Dhyana Stotram: Bhairava is the complete form of Shiva, and those who miss it are deluded by Shiva's own maya.
The Ganesha bija mantra, built on the seed syllable gaṃ given in the Ganapati Atharvashirsha.
The verse that asks the question a devotional platform has to sit with: in a reality of that kind, who exactly is being worshipped?
The first of the 112 techniques: the two ends of the breath, and the two silences the text says Bhairava's body shows itself in.
The five-verse visualisation of Batuka Bhairava, the child form called Apaduddharaka — 'he who lifts one out of calamity'. Recited before his hundred and eight names.
The four-bija invocation that opens each decade of the Kalabhairava Ashtottarashatanamavali, the hundred and eight names.
The seven-bija mantra of Mahakala Bhairava, given in the mantra section of the Ashta Bhairava Dhyana Stotram.
The nine-syllable Devi mantra used in the recitation of the Durga Saptashati.