Core Inclusion Criteria:

          1. ECOG performance status 0 or 1 with no deterioration over the previous 2 weeks

          2. Estimated life expectancy of greater than 12 weeks

          3. Ability to swallow and retain oral medication

          4. Women either of non-childbearing potential or of childbearing potential willing to
             practice effective contraception for the duration of the study and for 6 months
             (Module 1, Module 4) and 24 months (Module 2) after the last dose of CT7001

          5. Sexually active male patients must be willing to use condoms with all sexual partners
             for the duration of the study and for 3 months after the last dose of CT7001.

          6. Provision of signed and dated, written informed consent

        Core Exclusion Criteria:

          1. Any other malignancy that has been active or treated within the past 3 years, with the
             exception of cervical intraepithelial neoplasia and non-melanoma skin cancer

          2. Any unresolved toxicity (except alopecia) from prior therapy of ≥ CTCAE Grade 2

          3. Spinal cord compression or brain metastases, unless asymptomatic, stable, and not
             requiring steroids for at least 4 weeks before the first dose of investigational
             product (IP)

          4. Refractory nausea and vomiting, chronic gastrointestinal (GI) disease or previous
             significant bowel resection, with clinically significant sequelae that would preclude
             adequate absorption of CT7001

          5. Uncontrolled seizures

          6. Active infection requiring systemic antibiotic, antifungal, or antiviral medication

          7. Severe or uncontrolled medical condition or psychiatric condition

          8. Active bleeding diatheses

          9. Renal transplant

         10. Known hepatitis B, hepatitis C, or human immunodeficiency virus infection

         11. Breastfeeding or pregnancy

         12. Receipt of systemic cytotoxic treatment for the malignancy within 28 days or ≤ 5
             half-lives, whichever is shorter before the first dose of IP

         13. Receipt of non-cytotoxic treatment for the malignancy within 5 half-lives of the drug
             before the first dose of IP

         14. Receipt of corticosteroids (at a dose > 10 mg prednisone/day or equivalent) within 14
             days before the first dose of IP

         15. Receipt of any small-molecule investigational medicinal product (IMP) within 28 days
             or ≤ 5 half-lives, whichever is shorter before the first dose of IP

         16. Receipt of any biological IMP (e.g., immune checkpoint blockers, antibodies,
             nanoparticles) within 42 days before the first dose of IP

         17. Receipt of St John's Wort within 21 days before the first dose of IP or of another
             concomitant medication, herbal supplement, or food that is a strong inhibitor or
             inducer of CYP3A4, CYP2C19, CYP2D6, or P-glycoprotein (PGP) activity within 14 days
             before the first dose of CT7001

         18. Receipt of a blood transfusion (blood or blood products) within 14 days before the
             first dose of IP

         19. Known hypersensitivity to CT7001 or any excipient of the product

         20. Impaired hepatic or renal function as demonstrated by any of the following laboratory
             values:

               1. Albumin < 30 g/L

               2. Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) > 2.5 × the
                  upper limit of normal (ULN)

               3. > 5.0 × ULN for patients with liver metastases

               4. Total bilirubin > 1.5 × ULN

               5. Serum creatinine > 1.5 × ULN

         21. Liver function deteriorating in a manner that would likely make the participant meet
             the AST, ALT, or bilirubin levels specified above at the time of the first dose of IP

         22. Other evidence of impaired hepatic synthesis function

         23. Inadequate bone marrow reserve or organ function as demonstrated by any of the
             following laboratory values:

               1. Absolute neutrophil count (ANC) < 1.5 × 10^9/L

               2. Platelet count < 100 × 10^9/L

               3. Haemoglobin < 90 g/L

         24. Persistent (> 4 weeks) severe pancytopenia due to previous therapy rather than to
             disease (ANC < 0.5 × 10^9/L or platelets < 50 x 10^9/L)

         25. Cardiac dysfunction (defined as myocardial infarction within 6 months of study entry,
             New York Heart Association Class II/III/IV heart failure, unstable angina, unstable
             cardiac arrhythmias, or left ventricular ejection fraction < 55 percent)

         26. Mean resting QT interval corrected for heart rate by the Fridericia formula (QTcF) >
             470 msec obtained from 3 electrocardiograms (ECGs) obtained within 5 minutes of each
             other prior to the first dose

         27. Any clinically important abnormalities in rhythm, conduction, or morphology on resting
             ECG (e.g., complete left bundle branch block, third degree heart block). Controlled
             atrial fibrillation (AF) is permitted

         28. Any factor that increases the risk of QTc prolongation or of arrhythmic events (e.g.,
             heart failure, hypokalaemia, congenital long QT syndrome, immediate family history of
             long QT syndrome or unexplained sudden death under 40 years of age)

         29. In the opinion of the Investigator, unlikely to comply with study procedures,
             restrictions, or requirements

         30. A history of haemolytic anaemia or marrow aplasia

         31. Has received a live-virus vaccination within 28 days or less of planned treatment
             start

        Additional Module 1A Inclusion Criteria:

          1. Histological, radiological or cytological confirmation of an advanced
             non-haematological malignancy not considered to be appropriate for further standard
             treatment

          2. Module 1A biopsy cohort only : at least one tumour suitable for repeat biopsy

        Additional Module 1A Exclusion Criteria:

        1. International normalised ratio (INR) ≥1.5

        Additional Module 1B Inclusion Criteria

          1. Histological or cytological confirmation of metastasis or locally advanced tumour

          2. At least one line of systemic anti-cancer therapy

          3. Disease measurable by RECIST v1.1

        Additional Module 1B-1 (TNBC Expansion) Inclusion Criteria:

          1. Histologically-confirmed carcinoma of breast not expressing oestrogen receptor (ER) or
             progesterone receptor (PR) and negative for human epidermal growth factor receptor 2
             (HER2)

          2. Documented disease progression on or within 6 months of most recent cytotoxic prior
             cytotoxic chemotherapy

          3. Disease measurable by RECIST v1.1

          4. Must have received at least one cytotoxic chemotherapy for metastatic/locally advanced
             disease

        Additional Module 1B-1 (TNBC Expansion) Exclusion Criteria:

          1. No more than three lines of cytotoxic chemotherapy for metastatic/locally advanced
             disease

          2. No advanced, symptomatic visceral metastases

          3. No known symptomatic central nervous system (CNS) metastases, carcinomatous meningitis
             or leptomeningeal disease

          4. Prior exposure to CT7001

          5. Patients who are investigational site staff members directly involved in the conduct
             of the trial and their family members, site staff members otherwise supervised by the
             Investigator, or patients who are Carrick employees directly involved in the conduct
             of the trial

        Additional Module 2 Inclusion Criteria:

          1. Women only

          2. Pre- or peri-menopausal women must have initiated LHRHa at least 28 days prior to
             first dose of CT7001/placebo

          3. Histologically-confirmed, metastatic or locally advanced, ER+ve and/or PGR+ve and
             HER2-ve breast cancer

          4. Part A only: Disease measurable by RECIST v1.1

          5. Documented objective disease progression while on, or within 6 months after the end
             of, the most recent therapy

          6. Must have received an aromatase inhibitor together with a CDK4/6 inhibitor in the same
             line of therapy for locally advanced or metastatic disease or for treatment of early
             breast cancer if the disease-free interval was <12 months.

          7. For Part B only: patients must have received at least 6 months clinical benefit with
             the CDK4/6 as a line of therapy immediately preceding study entry. Patients who
             received CDK4/6 inhibitor < 6 months due to tolerability issues when at least 6 months
             aromatase inhibitor was received.

          8. Ability to receive intramuscular injections.

        Additional Module 2 Exclusion Criteria:

          1. Prior therapy with fulvestrant

          2. More than 2 lines of endocrine treatment for locally advanced or metastatic disease

          3. Part A Only: Prior treatment with more than one line of cytotoxic chemotherapy for
             locally advanced or metastatic breast cancer.

          4. Part B Only: Prior treatment with cytotoxic chemotherapy for locally advanced or
             metastatic breast cancer or treatment with a mammalian target of rapamycin (mTOR)
             inhibitor including, but not limited to, everolimus.

          5. Patients with liver metastasis will be limited to approximately 30-40% of the enrolled
             patients. l

          6. Known hypersensitivity to CT7001, fulvestrant or any excipient of the investigational
             products

          7. Patients who are investigational site staff members directly involved in the conduct
             of the trial and their family members, site staff members otherwise supervised by the
             Investigator, or patients who are Carrick employees directly involved in the conduct
             of the trial

        Additional Module 4 Inclusion Criteria:

          1. Patients must be able to eat a high-fat meal, as provided by the study site, within a
             30-minute period

          2. Histological, radiological or cytological confirmation of an advanced
             non-haematological malignancy not considered to be appropriate for further standard
             treatment

        Additional Module 4 Exclusion Criteria:

        1. Patients who were unable to fast for at least 10 hours

        Additional Module 6 Inclusion Criteria:

        1. Histological, radiological or cytological confirmation of an advanced non-
        haematological malignancy not considered to be appropriate for further standard treatment.

        Additional Module 6 Exclusion Criteria:

          1. Any concurrent gastrointestinal conditions, not covered in Core Protocol Exclusion
             Criteria #4

          2. Patients whom has received an agent that increases gastric pH (i.e. proton pump
             inhibitors (PPI), H2 antagonists) within 2 days or 5 half-lives, whichever is shorter,
             prior to PK Period Day 1.