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Iwasawa algebras of compact  p -adic Lie groups are completed group algebras with applications in number theory in studying class numbers of towers of number fields and representation theory of  p -adic Lie groups. We previously determined an explicit presentation of the Iwasawa algebra for the first principal congruence kernel of Chevalley groups overℤ  p{\mathbb{Z}_{p}}    which were uniform pro- p  groups in the sense of Dixon, du Sautoy, Mann and Segal. In this paper, for primep  &gt;   n  +  1{p&gt;n+1}   , we determine the explicit presentation, in the form of generators and relations, of the Iwasawa algebra of the pro- p  Iwahori subgroup ofGL  n   ⁢   (   ℤ  p   ){\mathrm{GL}_{n}(\mathbb{Z}_{p})}    which is not, in general, a uniform pro- p  group.

Explicit presentation of an Iwasawa algebra: The case of pro- p Iwahori subgroup of SL n (ℤ p )