Background: GM1 gangliosidosis is a disorder that destroys nerve cells. It is fatal. There is no treatment. People with GM1 are deficient in a certain enzyme. A gene therapy may help the body make this enzyme. This could improve GM1 symptoms. Objective: To test if a gene therapy helps Type I and Type II GM1 gangliosidosis symptoms. Eligibility: Type I subjects will be male and female \>= 6 months \<= 12 months of age at the time of full ICF signing. Type II subjects will be male and female \> 12 months old and \< 12 years old at the time of full ICF signing. Design: Participants will be screened with their medical history and a phone survey. Participants will stay at NIH for 8-10 weeks. Participants will have baseline tests: Blood, urine, and heart tests Hearing tests Ultrasound of abdomen EEG: Sticky patches on the participant s head will measure brain function. Lumbar puncture: A needle will be stuck into the participant s spine to remove fluid. MRI scans, bone x-rays, and bone scans: Participants will lie in a machine that takes pictures of the body IQ tests Neurology exams Central line placement Skin biopsy: A small piece of the participant s skin will be removed. Speech tests Participants will have an x-ray while swallowing food. Participants will take drugs by mouth and IV. This will get their immune system ready for therapy. Participants will get the gene therapy by IV. They may stay at NIH for a week to watch for side effects. Participants will have visits 3 and 6 months after treatment. Then visits will be every 6 months for 2 years. Then they will have a visit at 3 years. Visits will take 4-5 days. Participants will return to NIH once a year for 2 years for tests in an extension study....