Here’s my translation

Alan

1. Formáli.
1. Prologue.

Atburðir margir, þeir er verða, falla mönnum oft ór minni, en sumir eru annan veg sagðir en verit hafa, ok trúa því margir, er logit er, en tortryggja þat satt er.
Many (margr, Z2) events, those which happen, often fall out-of (the) memory of people (ie they are forgotten), but (and) some (events) are said (ie told) another way (ie otherwise) than to have (actually) been (ie they are misreported), and many (people) believe that which is lied (pp of ljúga) (ie falsehoods), but (and) (they) mistrust that (which) is true. (never more true than nowadays)

En fyrir því, at aftr hverfr lygi, þá er sönnu mætir, þá ætlum vér at rita nökkura atburði, þá er gerzt hafa á várum dögum á meðal vár kunnra manna, sem vér vitum sannleik til.
But for that (reason), that a lie turns back, when (it) meets (moeta) proof (sanna) (‘a lie recoils before the truth’, hverfa, Z3), then we intend to write certain events, those which have come to pass (görast) in our days among us familiar (known) people (ie our contemporaries), which we know (the) verity (sannleikr) of.

Í þeim atburðum mun sýnast mikil þolinmæði guðs almáttigs, sú er hann hefir hvern dag við oss, ok sjálfræði þat, er hann gefr hverjum manni, at hverr má gera þat, sem vill, gott eða illt.
In those events (the) great forbearance of God almighty will appear (manifest itself), that (forbearance) which he has (maintains, hafa, Z5) each day with us, and that liberty (free-will), which he gives to each person, (so) that each (person) may do that which (he or she) wants, good or evil (bad).