Traditionally, there are five or six texts included in Nagarjuna's works on reasoning.
Nagarjuna's most famous text is his Mulamadhyamakakarika, or Root Verses of the Middle Way, which presents in twenty-seven chapters an initially challenging, but extremely clear reasoning of how beings lack inherent existence and how this lack extends to samsara, nirvana, and even Buddha. While both historically and today, focus on the reasoning and the intellectual exercises this work promotes, it is more practical than that. As His Holiness the Dalai Lama has said, the verses are "a great source of inspiration, for they suggest that each of us has the opportunity to scale the greatest spiritual heights, provided we tread the right path."
There are many translations available, including The Ornament of Reason, which includes the famous commentary by Mabja Jangchub Tsondru, the twelfth-century Tibetan master and one of the first Tibetans to rely heavily on Nagarjuna's student Chandrakirti for his analysis.
An excellent contemporary commentary on the Mulamadhyamakakarika is Khenpo Tsultrim Gyamtso's The Sun of Wisdom. Focusing on the most important root verses, it is a very accessible entryway into this fundamental but challenging text.
As Khen Rinpoche says,
all the verses in this book are excellent supports for developing your precise knowledge of genuine reality through study, reflection, and meditation. You should recite them as much as possible, memorize them, and reflect on them until doubt-free certainty in their meaning arises within. Then you should recall their meaning again and again, to keep your understanding fresh and stable. Whenever you have time, use them as the support for the practices of analytical and resting meditation. If you do all of this, it is certain that the sun of wisdom will dawn within you, to the immeasurable benefit of yourselves and others.
Nagarjuna's Shunyatasaptati, or Seventy Stanzas on Emptiness (there are actually seventy-three), is really an expansion of the seventh section of the Root Verses, "Analysis of Characteristics of the Conditioned," that addresses some questions people had about the presentation of conditioned phenomena and whether that conflicted with sutra teachings. As is often the case, the answer lies in the difference between the conventional point of view of beings and how things actually are.
A translation of this work together with a commentary by Geshe Sonam Rinchen is available as Nagarjuna's Seventy Stanzas: A Buddhist Psychology of Emptiness.
Of the remaining texts in this category, Nagarjuna's Yuktisastika, or Sixty Verses on Reasoning, has been translated by Joseph Loizzo as Nagarjuna's Reason Sixty and is available from Columbia University Press. The Vigrahavyavartani, or Refutation of Objections, was translated most recently by Jan Westerhoff and published as The Dispeller of Disputes by Oxford University Press. And lastly, Nagarjuna's Vaidalyaprakarana is included in Nagarjuniana by Christian Lindtner, published by Motilal Banarsidass.