This paper presents an unsupervised method for learning cross-lingual word embeddings without requiring parallel data or bilingual dictionaries. The approach uses adversarial training to learn a linear mapping between monolingual word embedding spaces of two languages. The method is then refined using Procrustes optimization to improve alignment. The approach is evaluated on several cross-lingual tasks, including word translation, sentence translation retrieval, and cross-lingual word similarity. The results show that the method achieves performance comparable to or better than supervised approaches on several language pairs, including distant language pairs like English-Russian and English-Chinese. The method is also effective for low-resource language pairs, such as English-Esperanto, where parallel data is limited. The approach is shown to be effective in unsupervised machine translation tasks, as demonstrated by its performance on the English-Esperanto Tatoeba corpus. The method is evaluated on multiple benchmarks, including the MUSE library and the SemEval 2017 task, and outperforms previous approaches in several cases. The paper also introduces a cross-domain similarity local scaling (CSLS) method to mitigate the hubness problem in cross-lingual word embeddings. The method is shown to significantly improve the accuracy of word translation tasks. The paper concludes that the proposed approach is effective for cross-lingual word embeddings and can be used as a first step towards unsupervised machine translation.This paper presents an unsupervised method for learning cross-lingual word embeddings without requiring parallel data or bilingual dictionaries. The approach uses adversarial training to learn a linear mapping between monolingual word embedding spaces of two languages. The method is then refined using Procrustes optimization to improve alignment. The approach is evaluated on several cross-lingual tasks, including word translation, sentence translation retrieval, and cross-lingual word similarity. The results show that the method achieves performance comparable to or better than supervised approaches on several language pairs, including distant language pairs like English-Russian and English-Chinese. The method is also effective for low-resource language pairs, such as English-Esperanto, where parallel data is limited. The approach is shown to be effective in unsupervised machine translation tasks, as demonstrated by its performance on the English-Esperanto Tatoeba corpus. The method is evaluated on multiple benchmarks, including the MUSE library and the SemEval 2017 task, and outperforms previous approaches in several cases. The paper also introduces a cross-domain similarity local scaling (CSLS) method to mitigate the hubness problem in cross-lingual word embeddings. The method is shown to significantly improve the accuracy of word translation tasks. The paper concludes that the proposed approach is effective for cross-lingual word embeddings and can be used as a first step towards unsupervised machine translation.