SND@LHC is a proposed, compact and stand-alone experiment to perform measurements with neutrinos produced at the LHC in an hitherto unexplored pseudo-rapidity region of $7.2 < \eta < 8.6$, complementary to all the other experiments at the LHC. The experiment is to be located 480 m downstream of IP1 in the unused TI18 tunnel. The first phase aims at operating the detector throughout LHC Run 3 to collect a total integrated luminosity of 150 fb$^{−1}$. Following the review of the Letter of Intent [1], submitted in August 2020, LHCC recommended the collaboration to proceed with the preparation of a Technical Proposal (TP), reported herein.