1817 lectures
PhilPapers translates the title as Lectures on Logic and Metaphysics (from Wyss's announcement of the find in Hegel-Studien). Here is the German edition Vorlesungen über Logik und Metaphysik,
Heidelberg 1817, Hamburg: Meiner (1992). The publisher's description explains (my translation):
"It was not until 1984 that the postscript of a lecture on logic and metaphysics from the summer semester of 1817 was found in a Swiss private archive, transcribed by the law student Franz Anton Good. This transcription is based on a dictation and testifies, with great authenticity, to the expression and thought of Hegel, who here refers, in outline, to the conception of Encyclopedia of Philosophical Sciences, the first part of which was published that semester."
Reviews by Kruck and by Comoth, also in German, are available on ProQuest. I do not believe there is an English translation. Nothing comes up on Google Scholar, and Ficara's commentary Hegel on the Interplay between Logic and Metaphysics (2016) cites the German edition. Here is some of her commentary:
"In the Lectures on Logic and Metaphysics of 1817 Hegel maintains that not only the forms of thought,
but also their truth, constitute the research field of logic. This also implies that logical forms are
necessarily linked to nature and natural language: “Logic is for us a natural metaphysics. Everyone
who thinks has it. Natural logic does not always follow the rules which are established in the logic as
theory; these rules often trample on natural logic”. (Logik und Metaphysik 1817, p. 8).
Significantly, Hegel distinguishes between logic as theory and logic as natural logic or natural
metaphysics. First, he underlines the role of concrete experience (natural logic and natural
metaphysics) for the discovery and fixation of logical rules in the logical theory; second, he
understands experience in an expanded way as already structured by language and thought (natural
logic and natural metaphysics). This conception perfectly coheres with Hegel’s Aristotelianism, as
Hegel repeatedly underlines that Aristotle’s empiricism is speculative (Verra 2007, p. 364)."
1801-02 lectures
From what is sometimes referred to as "Hegel's Lectures on Logic and Metaphysics from the winter semester 1801-1802" we only have Troxler's notes (found in 1970-s) Schellings Und Hegels Erste Absolute Metaphysik, Zusammenfassende Vorlesungsnachschriften von I.P.V.Troxler. Köln, Jürgen Dinter, 1988. No luck with an English translation either, there is a Russian one online. Here is Olivier's review, in German, and English commentary in Siep's chapter 4 from Cambridge's Hegel's Phenomenology of Spirit. According to Siep:
"Hegel is here continuing his Differenzschrift criticism of Reinhold and Bardili, who attributed such an introductory and foundational role [in coming to know the absolute] to logic, as the theory of the forms of thought. The crucial task is precisely to overcome such a separation of form and content and, indeed, the very dichotomous structure - the "fixed oppositions" - of the fundamental concepts of logic and ontology. The only thing an introduction to philosophy, conceived as the knowledge of the absolute, can accomplish is to demonstrate the one-sidedness or "subjectivity" of every other standpoint apart from actual knowledge of the absolute. Hegel's first systematic implementation of this function of the introduction is to be found in the Phenomenology itself."
