Key inclusion criteria:

          1. Ages Eligible for Study: 18 Years and older

          2. Sexes Eligible for Study: All

          3. ECOG performance status of 0 to 1

          4. Patients are defined as follows:

             a) Phase 1a study will enroll patients with HER2-positive advanced solid tumor ; Phase
             1b study will enroll patients with HER2-positive advanced breast cancer.

             i.HER2-positive is defined as Immunohistochemistry (IHC) (++) and Fluorescence In Situ
             Hybridization (FISH) positive, or IHC (+++).

             ii.For patients who have no brain metastases, the following criteria should be met:
             (1) Patients should be relapsed or refractory to existing therapy(ies) known to
             provide clinical benefit for the underlying cancer or have been intolerant of such
             therapies (2) Have at least one extracranial measurable lesion per RECIST v1. 1 iii.
             For patients with brain metastasis, the following criteria should be met: (1) Have
             received prior treatment or declined the above treatment according to the protocol
             requirements; (2) Patients with HER2-positive gastric cancer must have previously
             received Trastuzumab (3) Do not require immediate local treatment during the trial
             period according to the protocol requirements.

             iv. For patients who have received previous tyrosine kinase inhibitor (TKI) treatment
             or chemotherapy, the interval between the last treatment and the first administration
             of the study drug in this trial should be at least 3 weeks. For patients who receive
             antibody or antibody-drug conjugate (ADC), the interval between the last treatment and
             the first administration of the study drug in this trial should be at least 4 weeks.

             b) Phase 1c study will enroll patients with HER2-positive breast cancer with brain
             metastases:

             i. HER2 positive is defined as IHC (++) and FISH positive, or IHC (+++);

             ii. Patients do not require immediate local treatment during the trial period
             according to the protocol requirements.

             iii. Patients should have at least one measurable intracranial lesion accurately
             measured at baseline by magnetic resonance imaging (MRI).

          5. Life expectancy ≥6 months;

          6. Have adequate organ and bone marrow function within 7 days before the first
             administration according to the protocol

          7. Man of reproductive potential or women of child-bearing potential shall be use of
             highly effective methods of birth control (such as oral contraceptives, intrauterine
             contraceptive device, abstinence or barrier contraception in combination with
             spermicide) during the trial, and continue to practice contraception for 3 months
             after the last administration.

          8. Subject or legally authorized representative of a subject must provide signed informed
             consent document, have good compliance, and are cooperative with the follow-ups.

        Key exclusion criteria:

          1. Subjects who have participated in any clinical study or received any clinical study
             drug within 4 weeks prior to the first administration;

          2. Based on screening brain MRI, any of the following criteria for patients with brain
             metastasis:

               1. progressive neurologic impairment or increased intracranial pressure

               2. any intracranial lesion thought to require immediate local therapy

               3. require antiepileptic treatment

          3. Subjects who have opportunistic infection or progressive (severe) infection

          4. Subjects who have undergone large surgeries within 4 weeks prior to the initiation of
             treatment or need large surgeries during the trials (excluding biopsy);

          5. Subjects who have intracranial hemorrhage or stroke within 6 months prior to the first
             administration;

          6. Subjects who have active gastrointestinal disorders or other diseases, which may
             significantly affect the absorption, distribution, metabolism or excretion of
             ZN-A-1041;

          7. Subjects who are currently using (or will not discontinue at least 1 week prior to the
             first administration of the trial) any drug or herbal medicine known to inhibit or
             induce CYP3A4 and CYP2C8 activity;

          8. Subjects who meet one of the following cardiac criteria:

               1. Congestive heart failure (New York Heart Association functional classification)
                  of ≥ 2

               2. Peripheral arterial disease (PAD), like Coronary artery disease, hypertrophic
                  cardiomyopathy (HCM)or Dilated cardiomyopathy

               3. Abnormalities in the ECG Measurements: such as First-degree heart block,
                  Second-degree heart block, Third-degree heart block, Prolonged PR: > 0.20s

               4. Any clinically significant supraventricular arrhythmia or ventricular arrhythmia
                  requiring treatment or intervention

               5. Angina requiring treatment

               6. Myocardial infarction within the past 12 months

               7. Percutaneous transluminal coronary angioplasty/stenting (PTCA), coronary artery
                  bypass graft (CABG) within 6 months of the first dose of the study treatment

               8. QTcF prolongation (> 470 ms for women and > 450 ms for man
                  (Fridericia-corrected)), a known history of QTcF prolongation or Torsade de
                  Pointes; or is on drugs that are required for existing medical conditions and
                  that may result in QT prolongation (e.g., anti-arrhythmic drugs)

          9. Subjects who have not fully recovered from previous treatment and still has CTCAE
             grade 1 or higher AEs, excluding alopecia. prior to the first administration;

         10. Pregnant or lactating women

         11. Subjects who are known to be allergic to ZN-A-1041 and its metabolites or its
             pharmaceutical excipients (active or not)

         12. Subjects who have serious accompanying diseases or an abnormal laboratory finding.

         13. Subjects who have serious psychological or mental abnormalities.

         14. Subjects who have complications of the central nervous system which require urgent
             neurosurgical interventions.